Why does Nick tell Gatsby's story in The Great Gatsby?

Arguably, Nick is the narrator of The Great Gatsby because he is an outsider. Nick is not from West or East Egg, for instance, and was, in fact, raised in the Midwest. In addition, Nick does not have the same wealth or status as Gatsby. 
Secondly, Nick is also the narrator of Gatsby's story because he is a non-judgemental type of person, as he admits in the opening chapter:

"I’m inclined to reserve all judgments, a habit that has opened up many curious natures to me."

This makes him the ideal person to tell Gatsby's story because he approaches it with honesty and objectivity. 
Moreover, when Nick finally gets an invitation to one of Gatsby's famous parties, he does not act like the other people there. He actively seeks Gatsby out, for example, and wants to know more about the man himself instead of the persona he has created. 

Nick tells the story of Jay Gatsby because he is arguably the most objective character in the novel. Also, since he has no previous knowledge of Gatsby, Nick can narrate in less of a chronological order than one would expect from those who have been acquainted with him.
As the readers learn about Gatsby in bits and pieces of background mixed with current knowledge, Nick tells readers about Gatsby in non-linear order that is typical of the Modernist movement in literature. In addition, this style of narration also seems more believable because this is the order in which one normally learns about someone. And, for Nick to repeat the fabrications of Jay--such as his war record--lends a trust factor to the narration because he is more naive about Gatsby than others. As he declares, "I am one of the few honest people that I have ever known."
In addition, Nick is a person whom others trust. However, Nick, too, becomes entangled as his own romantic naivete causes him to give more credibility to Gatsby than he would any other character or would an omniscient narrator. Yet, this credibility of Gatsby makes him "great," a man who believes that he can repeat the past and improve upon it.
With the assistance of Nick Carraway as narrator, Gatsby comes alive as a romantic hero. In Chapter Four, Nick narrates,

Then it had not been merely the stars to which he had aspired on that June night. He came alive to me, delivered suddenly from the womb of his purposeless splendor.

But, this romantic hero deteriorates for Nick, and he becomes disillusioned, thinking of returning to the Midwest where he can "run faster" and transcend the past and recreate the past.