George Wilson commits suicide with the same gun he uses to murder Gatsby. As Gatsby floats on a raft in his swimming pool, Wilson shoots him several times, killing him. Nick, along with Gatsby's chauffeur, butler, and gardner, finds Gatsby's body first, then discovers Wilson's "a little way off in the grass." Nick says "the holocaust was complete."
The other answer I am afraid is wrong. She has taken a very simplistic view which to be honest the majority of the readers do aswell. At first glance it seems that Gatsby has been killed by Wilson when in fact Fitzgerald, the author, has disguised the murder with a few lines that point at Wolfshiem being the murderer. Read the end of chapter 8 again and try to spot how wolfshiem could have in fact been the killer. Now, it is extremely complex and many academics have failed to truly express themselves correctly when they have tried to describe the murder scene, therefore, I will try to be as simplistic as possible. Focus on this line, "The chauffeur - he was one of Wolfshiem's proteges - heard the shots - afterwards he could only say that he hadn't thought anything much about them." This suddenly changes everything, as if they had heard the shots then surely they would have done something about it. Wolfshiem as a whole is a very dodgy character, in the notes at the end of the book it states that Meyer Wolfshiem was based on the famous gambler Arnold Rothstein who Fitzgerald believed to have fixed the Baseball event. Not only is he a strange character but he also does not turn up to Gatsby's funeral having supposedly been very close to him and a "great business partner". More reason to be suspicious, the fact that Wilsons proteges were even nearby suggests that they were trying to 'set up' a murder scene. They must have shot Wilson and taken him to Gatsby where they left him "a little way off in the grass". This is proven by the fact that Wilson could not afford a rifle whereas Wolfshiem could have. He later writes a letter to Nick explaining why he cannot attend the funeral. This is where our suspicions become real. In his letter he tries to make it very obvious that it was Wilson who shot him as well as the tone being false and insensere. He talks about "things" and "etc" which implies he is being fake. He then finishes off by making vague reasons why he could not attend the funeral, therefore putting business first. Putting business first would have been the same theory used in order to kill Gatsby.
Fitzgerald is a fantastic writer and he would not have made it as simple as Wilson just being the killer. He include Wolfshiem in the novel for a reason. Just think about it. Read over that last few pages and it should become clearer. Hope that helped!