Readers do not actually learn who gets Gatsby's money when he dies. Of course, he does not have any children or obvious heirs to inherit his wealth, but it turns out that he does not really have many close friends either, besides Nick. He did not really know the people who came to his parties, and they certainly do not show up for him in the end, as shown by the poor turnout at his funeral. We might assume that he would not leave the money to Meyer Wolfshiem, because his former business associate and "friend" has quite enough money of his own, and it doesn't appear that they were overly close.

Nick gives no indication that Gatsby leaves anything to him, and it seems unlikely Gatsby would leave the money to Daisy, who is plenty rich already and ultimately chose her husband Tom over Gatsby.

It seems most likely that, being his only living relative, Gatsby's father would inherit his fortune. That said, there is nothing explicitly stated in the book to prove this. When Gatsby's father comes to West Egg to attend his son's funeral, he mentions that Gatsby had gone to visit him about two years earlier and actually bought him the home in which he currently lives. Gatsby grew up poor, and it seems that he was determined to help his parents, too, once he made enough money to do so.