Where did the religious symbol of the 'halo' come from?

A halo is an aureola. Aureoles pertain to the various degrees of glory/merit the saints, with their resurrected (glorified) bodies, may have:

        color:  victor over:
martyr: red     world
virgin: white   flesh
doctor: green   devil

Answering the question "Whether an aureole is also due to the body?" (Summa Theologica suppl. q. 96 ("Of the Aureoles") a. 10 co.), St. Thomas Aquinas writes:

Properly speaking the aureole is in the mind: since it is joy in the works to which an aureole is due. But even as from the joy in the essential reward, which is the aurea, there results a certain comeliness in the body, which is the glory of the body, so from the joy in the aureole there results a certain bodily comeliness: so that the aureole is chiefly in the mind, but by a kind of overflow it shines forth in the body.

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_{[Latin:] aureola proprie est in mente, est enim gaudium de operibus illis quibus aureola debetur. Sed sicut ex gaudio essentialis praemii, quod est aurea, redundat quidam decor in corpore, qui est gloria corporis; ita ex gaudio aureolae resultat aliquis decor in corpore; ut sic aureola principaliter sit in mente, sed per quamdam redundantiam fulgeat etiam in carne.}

Thus, halos don't originate from art or pagan beliefs but from the Church's teaching on the resurrection of the body and merit (reward for practicing virtue)

If you have no credible source for this idea, then why do you mention it? It is impossible to prove that the first iconographers to use halo didn't take inpirations from pagan imaginery.

In order to know if halo is compatible with christian faith, you have to look what is the meaning of light in Scriptures. You can see from many fragments (like The Gospel According to St Jonh the Theologian Prologue) that the light means the life-giving energy of God. We can see that Christ shone with light during His transfigurations. We see prophets seeing light during their revelations. This is why Christ is surrounded by halo in icons (in the icon of Transfiguration this halo is big and surrounds His whole body).

Also the holy men (I don't know why you use quotes here) could be seen shining this light. There is a wonderful example in this text: St. Seraphim of Sarov's Conversation With Nicholas Motovilov.

Father Seraphim replied: "I have already told you, your Godliness, that it is very simple and I have related in detail how people come to be in the Spirit of God and how we can recognize His presence in us. So what do you want, my son?"

"I want to understand it well," I said.

Then Father Seraphim took me very firmly by the shoulders and said: "We are both in the Spirit of God now, my son. Why don't you look at me?"

I replied: "I cannot look, Father, because your eyes are flashing like lightning. Your face has become brighter than the sun, and my eyes ache with pain."

Father Seraphim said: "Don't be alarmed, your Godliness! Now you yourself have become as bright as I am. You are now in the fullness of the Spirit of God yourself; otherwise you would not be able to see me as I am."

(I would recommend to reading the whole text)

So even if there was some pagan elements of inspiration in this symbol (like e.g. clergy vestments taking inspiration from the roman officials dresses), it is now used for the christian meaning and is fully compatible with what Christianity teaches.

The halo originated from the Pre-Islmaic Iranian faith of Zoroastrianism. They believed in the Idea of Farr, or "Divine Favor". this 'favor' was represented by a ring called the Hvrena which was given to the king by their gods, but if the king displeased the gods, it was taken away. This ring was guarded by the god Mithras, who was the god of Daylight. It was through the relation of the Hvrena with Mithras and a mistranslation of the word "Farr" which means glory, that brought about the idea that the halo, or ring of divine favor, was actually representing light. When Zoroastrianism traveled to the Roman Empire in the form of Mithraism, or the Mysteries of Mithras, the Hvrena was depicted as a halo on the head of Mithras. Christianity was developing at the same time as Mithraism, and artists would have seen halos in Mithraeum at the time. In the Roman Empire, it was common to practice more than one faith. Halos were not, however, used in Christian art until Mithraism was almost extinct.

My source for this is that I wrote a term paper about the origin of the Halo for my History of Christian Art course during my undergrad.

For more information on Farr and Hvrena, see this website: Encyclopedia Iranica.

For information on how it transitioned to Christian art, however, one needs to dig through many books, as no one has ever written a full book on this process.