This question represents a classic area of disagreement between Christians. There are two schools of thought and each holds tenaciously to their position. One says that each and every individual is personally responsible for their decision to make Christ Savior and Lord and their status as a born-again Christian is entirely one of their own free will.
The other side holds just as firmly to the belief that we are chosen beforehand through the sovereignty of God and predestined to be saved. They would say any “choice” we have in the matter is simply because we were chosen first by God.
The problem with this argument is that both sides of the debate boldly quote Scripture to back up their positions. As a result, most Christians feel compelled to side with one position or the other—whichever they feel defend their position with the most convincing evidence.
The solution to this conundrum—which seems to completely escape proponents of both sides—is one that does no violence to the body of Scripture. Put simply, both positions are equally true. Having said that, I am well aware there are many who believe what I have just said to be patently impossible. They themselves are unable to reconcile how they can be Christians resulting from both an act of their free will and God's predestination. Therefore they reject this conclusion out of hand.
But I would argue its validity from two perspectives:
1. It is biblical.
There's no question that the Bible speaks of God’s sovereign election (predestination) of the saints. Romans chapter eight is one very clear example. But there are, likewise, passages of Scripture which speak of the choice given to mankind. The King James version of the Bible renders Revelation 22:17 with the words, “…whosoever will, let him take the water of life freely.” The NIV says “…whoever wishes…” and the NKJV says “…whoever desires…” The idea is clearly set forth that there is a choice we face in receiving Christ as Lord. This idea is repeated many times throughout the Word of God.
2. The ability to reconcile these two ideas is not our responsibility.
Christians often fall into the trap of accepting or rejecting a truth based on whether or not they can personally comprehend it. This is always dangerous and holding to that idea may require you to take a scissors to your Bible. Can you comprehend eternity? How about the Trinity? Yet both are clearly revealed in God's Word.
At the end of the day, my responsibility is to prayerfully look into the Word of God and determine what truth it reveals, regardless of whether I can personally explain those truths from an intellectual standpoint. And what the Bible reveals about our salvation is that 1) God elected us for salvation according to His foreknowledge, and 2) we must choose (receive) Christ according to the gift of our free will. As for explaining how those two realities can coexist...that’s God’s problem, not mine.