Are there explicit statements in the New Testament about the purpose of life?

Paul states the purpose of (man's) life succinctly in his first epistle to Timothy (2:4): it is to be saved, and to come unto knowledge of the truth. This verse actually refers to God's desire for man, so one has to accept that God's purpose for our life is, in fact, its true purpose.

This is a simple verse, but Christian believers have widely differing views - some even based on the same Scriptures - as to what salvation entails and how exactly one comes unto knowledge of the truth. But I think the verse in 1 Timothy is probably the most straightforward New Testament Scripture that addresses the purpose of life.

In Acts 17:26-28, Paul is in Athens preaching the gospel. The Apostle says that God created humans from one blood and they are placed around the world so that they may seek the Lord and come to repentance. This appears to be one of the closest examples of the meaning of life from the New Testament. I can't say this is explicit, but it gets pretty close.

When a scribe asked Jesus what was the greatest commandment in the law, Jesus' answer quoted a law that expressed our whole purpose in life: "You shall love the Lord your God with all your heart, with all your soul, and with all your mind. This is the first and great commandment. And the second is like it: 'You shall love your neighbor as yourself.' On these two commandments hang all the Law and the Prophets." (Matthew 22:34-40.)

Unfortunately, people believe the laws in the Bible are to make a person righteous. Not so; rather, they are expressions of love to God and man; they tell us the many ways we can express love. This is our purpose: to love God and others.

A more explicit declaration of life purpose (using the phrase "whole duty of man") can be found in Ecclesiastes 12:13-14:

"Let us hear the conclusion of of the whole matter: Fear God and keep His commandments, for this is the whole duty of man. For God will bring every work into judgment, including every secret things, whether it is good or whether it is evil."

So, because we will be judged in the end, our purpose is to live in such a way as to pass such judgment. As noted here, that involves keeping God's laws, all of which are summed up in the Matthew passage quoted above.

God's purposes are eternal, therefore I believe the following is most relevant:

Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent. - John 17:3 NIV

This by no means excludes the other answers but is complementary to them, however seeking and repenting are very much time-bound activities, their fulfillment (true purpose) is in finding and abiding in Him.

Here are just a handful of New Testament verses relating to life purpose (based on Rick Warren's The Purpose Driven Life):

Revelation 4:11 (NLT): “You are worthy, O Lord our God, to receive glory and honor and power. For you created all things, and they exist because you created what you pleased.”

Hebrews 2:10A (NCV): God is the One who made all things, and all things are for his glory. He wanted to have many children share his glory

Colossians 1:15 (MSG): We look at this Son and see God’s original purpose in everything created.

John 17:4 (MSG): I glorified you on earth by completing down to the last detail what you assigned me to do.

Acts 20:24 (NCV): The most important thing is that I complete my mission, the work that the Lord Jesus gave me — to tell people the Good News about God’s grace.

These respectfully correspond to the 5 purposes that we've been given (based on the book mentioned above):

1. You were planned for God's pleasure
2. You were formed for God's family
3. You were created to become like Christ
4. You were shaped for serving God
5. You were made for a mission

The verses above are, of course, a very incomplete list. There are apparently 350 references to the Bible in The Purpose Driven Life which point to many more verses.

It's well worth the read for any that are interested in a more complete answer to the question of purpose from a Christian worldview, and it includes a great number of verses to support it.