What is the history of the concept of a "personal relationship with Jesus"?

Are you only after historical references of the exact phrasing?

As you mentioned clearly from the scriptures implicitly proclaim the reality of a personal and relational God, though those exact words are not uttered.

I'm keen to post just a few scriptures below in case anyone reading is considering that their faith is anything but a "personal relationship" with Jesus.

The Early Church also implicitly validate the idea that God is "relational" or "Personal".

Noverim te, noverim me: "I would know you [God], I would know myself." - Augustine

“He [Jesus] fought and conquered. On the one hand, he was man who struggled for his fathers and through his obedience cancelled their disobedience. On the other hand, he bound the strong one and freed the weak and bestowed salvation on his handiwork by abolishing sin. For he is our compassionate and merciful Lord who loves mankind ... Irenaeus of Lyons, Against Heresies 3

“The Glory of God is a human being fully alive.” ― Irenaeus of Lyons

The physical voice we use in prayer need not be great nor startling; even should we not lift up any great cry or shout, God will yet hear us. - Origen

We have been taught that God did not make the world aimlessly, but for the sake of the human race; and we have before stated that He takes pleasure in those who imitate His properties - Justin Martyr

++++SCRIPTURES++++

Jesus loves us For I am sure that neither death nor life, nor angels nor rulers, nor things present nor things to come, nor powers, nor height nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord. - Romans 8:38-39

Jesus wants to know us --- And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness!’ - Matt 7:23

Jesus wants us to love him --- Jesus said to him, “‘You shall love the Lord your God with all your heart, with all your soul, and with all your mind.’ - Matt 22:37

Jesus is our friend --- I do not call you slaves anymore, because a slave doesn't know what his master is doing. I have called you friends - John 15:15

Jesus lives in us --- Do you not know that you are God's temple and that God's Spirit dwells in you? - 1 Cor 3:16

Jesus helps, knows and is within us --- And I will ask the Father, and he will give you another Helper, to be with you forever, even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you. - 1 John 14:16-17

Jesus name mean's "God with us" --- “Behold, the virgin shall conceive and bear a son, and they shall call his name Immanuel” (which means, God with us). - Mat 1:23

Jesus wants us to follow him --- Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me. - John 14:6

Jesus is our home --- Jesus answered him, “If anyone loves me, he will keep my word, and my Father will love him, and we will come to him and make our home with him. - John 14:23

Jesus forgives us --- And when Jesus saw their faith, he said to the paralytic, “Son, your sins are forgiven.” - Mark 2:1-28

Jesus speaks to us --- My sheep hear my voice, and I know them, and they follow me. I give them eternal life, and they will never perish, and no one will snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of the Father's hand. I and the Father are one. - John 10:27-30

Jesus listens to us and bears our burdens --- Humble yourselves, therefore, under the mighty hand of God so that at the proper time he may exalt you, casting all your anxieties on him, because he cares for you. - 1 Peter 5:5-13

Jesus doesn't condemn us --- “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life. For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him. Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God. - John 3:16-18

Jesus encourages us --- Have I not commanded you? Be strong and courageous. Do not be frightened, and do not be dismayed, for the Lord your God is with you wherever you go.” - Josh 1:9

Jesus understands us --- Jesus understands every weakness of ours, because he was tempted in every way that we are. But he did not sin! 16 So whenever we are in need, we should come bravely before the throne of our merciful God. There we will be treated with undeserved kindness, and we will find help. - Hebrews 4:15-16

In the first letter from John, the first chapter, there something that could be interpreted as "personal relationship", with God and Jesus.

And truly our fellowship is with the Father and with His Son Jesus Christ. [...] If we say that we have fellowship with Him, and walk in darkness, we lie and do not practice the truth. But if we walk in the light as He is in the light, we have fellowship with one another, and the blood of Jesus Christ His Son cleanses us from all sin.

The word fellowship here is the greek koinōnia, which according to Strong has the following meaning:

partnership, that is, (literally) participation, or (social) intercourse, or (pecuniary) benefaction: - (to) communicate (-ation), communion, (contri-), distribution, fellowship.

So I do think the "personal relationship" is biblical and an early christian concept.

Jesus spoke of this personal relationship on at least two occasions. Here is text from John 14:15-26 with my emphasis:

15 “If you love me, you will obey what I command. 16 And I will ask the Father, and he will give you another Counselor to be with you forever— 17 the Spirit of truth. The world cannot accept him, because it neither sees him nor knows him. But you know him, for he lives with you and will be in you. 18 I will not leave you as orphans; I will come to you. 19 Before long, the world will not see me anymore, but you will see me. Because I live, you also will live. 20 On that day you will realize that I am in my Father, and you are in me, and I am in you. 21 Whoever has my commands and obeys them, he is the one who loves me. He who loves me will be loved by my Father, and I too will love him and show myself to him.”

22 Then Judas (not Judas Iscariot) said, “But, Lord, why do you intend to show yourself to us and not to the world?”

23 Jesus replied, “If anyone loves me, he will obey my teaching. My Father will love him, and we will come to him and make our home with him. 24 He who does not love me will not obey my teaching. These words you hear are not my own; they belong to the Father who sent me.

25 “All this I have spoken while still with you. 26 But the Counselor, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you.

Note here that:

• the personal relationship is not only with Jesus but also with The Father and The Holy Spirit.

• eating together was a particular sign of fellowship (or a relationship). Here the reference is to making a home but the second passage mentions eating together (Revelation 3:20):

Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with him, and he with me.

Just for clarity, this is after the Resurrection and Ascension, implying that this fellowship is available to all, not only those who met Jesus physically.

I think it's based on when did people start to use the phrase about religious or other subjects. It's not really a church history, but a English language history.

It turns out the earliest quote another group found was in 1864, but popularized much more recently into a cliche:

In this coming again of Christ by the Spirit, there is included also the fact that he will be known by the disciple, not only socially, but as the Christ, in such a way as to put us in a personal relationship with him, even as his own disciples were in their outward society with him.

Title: Christ and his salvation: in sermons variously related thereto (page 341)  Author:  Bushnell, Horace, 1802-1876.  Publication Info: New York,: 1864.  Collection: Making of America Books

You can read a similar discussion here.

I think the popularity of the phrase "personal relationship with Jesus", and "accepting Jesus into your heart" among evangelicals comes from the influence of a few evangelical figureheads in the past century such as Billy Graham, Bill Bright, and others.

However, the concepts themselves - when understood correctly - can certainly be found in very explicit terms within Scripture.

1) "A Personal Relationship with Jesus" - In speaking to this phrase let me first say what I believe the intent behind the phrase is, when most commonly used: The idea of a "personal relationship with Jesus" speaks primarily to the idea that a person does not just know about the historical character called Jesus the Christ in a purely historical or religious context. It speaks to the fact that the Gospel of Jesus Christ is the message that by placing one's trust in Jesus for the forgiveness of their personal sins they can have restored fellowship with God, and a direct relationship with him where God listens to the individual and relates to the individual through the Holy Spirit, through the Scriptures, and through the Body of Christ (the Church).

The phrase speaks to the personal nature of this relationship and how biblical Salvation is a personal process where God interacts individually with each of the people he is giving salvation to - not just in a generic and disconnected relationship to all of mankind.

While we do not read the words as such in the Scriptures, neither do we read any of our English words in the original text - all are an interpretation. But while we don't read these words even in our English interpretation, the concept behind them is very much present in many passages throughout the New Testamant.

So while I would assert that the actual words in question have been made popular by contemporary evangelical leaders (who started the exact linguistic combination of words I surely don't know), I would also argue that the concept which they actually represent is not unique to our culture, or some post-enlightenment thinking. The idea of personal salvation is very explicitly discussed in the Scriptures.

Here's a few of the passages in the New Testament that make the case:

Consider John 14:23-26 which emphasizes the incredibly interpersonal relationship between the person who loves Jesus and God, to the extent where Jesus describes coming and living inside that person:

Jesus replied:

If anyone loves me, they will obey me. Then my Father will love them, and we will come to them and live in them. But anyone who doesn’t love me, won’t obey me. What they have heard me say doesn’t really come from me, but from the Father who sent me.

I have told you these things while I am still with you. But the Holy Spirit will come and help you, because the Father will send the Spirit to take my place. The Spirit will teach you everything and will remind you of what I said while I was with you.

Also, consider Revelation 3:20 which again uses an unmistakably interpersonal analogy:

Listen! I am standing and knocking at your door. If you hear my voice and open the door, I will come in and we will eat together.

In the first century culture of the middle east, eating together was a very personal things. As much as we want to peg the enlightenment with being the source of our individualism (and it certainly was on a certain scale), it's not as though the idea of personal, intimate relationships were absent from society before that time period. In fact, one of the greatest demonstrations of a personal, intimate interaction you could have with another person in ancient culture was to eat a meal with them. It was a symbol of deep inner fellowship. So for Jesus to say "I will come in and we will eat together" is explicitly language of personal intimacy.

So though the words in our present form were not combined as such, the connotation certainly existed in very explicit terms in Scripture.

2) "Accepting Jesus into your heart" - Although you didn't ask about this phrase, it's very commonly used in conjunction with the other, so it's worth mentioning...

Now I don't know that this phrase in the cliche form it has become is particularly helpful in sharing the Gospel with others, but it certainly seems to have biblical basis for it's connotation.

The idea of "accepting Jesus into your heart", or "receiving Christ" comes from the biblical notion of "believing in Jesus," or as some translations say, "receiving him":

But as many as received Him, to them He gave the right to become children of God, to those who believe in His name. (John 1:12)

In the above passage from the Gospel of John, John is presumably referring to people who "reveived" Jesus as the Messiah, or Sent One from God. While many rejected Jesus (particularly the religious leaders), his own followers "accepted" him as God's Messiah.

Further, on a more conceptual level, the "heart" has long been considered by cultures to be a representative term for the "seat of emotion", or "the innermost part" of a person's being, or even the place where a person's love originates.

It also is used to represent a place of "authenticity" or "sincerity." If I say, "I mean it from the bottom of my heart," you know what I'm really trying to say is that I'm being authentic and sincere in the action or words associated with that.

So in this regard "accepting Jesus into your heart" may simply speak to a genuine and sincere belief or trust in Jesus as who is claimed to be, as opposed to an intellectual acknowledgement of his mere historical existence.

Finally, there is another very interesting passage in one epistle where I believe the specific wording about accepting him "into our hearts" may be actually derived from:

...so that Christ may dwell in your hearts through faith; and that you, being rooted and grounded in love, may be able to comprehend with all the [m]saints what is the breadth and length and height and depth, and to know the love of Christ which surpasses knowledge, that you may be filled up to all the fullness of God. (Ephesians 3:17-19)

As a point of commentary: All this being said, I believe both of these phrases when used in the cliche way that most of us have heard them serve little purpose in communicating the real nature of life in Christ. The trouble is that when they are used as a cliche way to tell somebody what it means to be a follower of Jesus, they are often an oversimplification of what the Gospel life is really about. They usually lead to some prayer to "accept Jesus into your heart" which is more akin to an incantation than to actually beginning a real walk with Christ.