Fury, 27, is the second Briton to win the award, after he shocked Ukrainian Wladimir Klitschko to claim the IBF, WBA and WBO titles in November.
"I can't believe I've just won Ring magazine fighter of the year," Fury said. "I'm so flattered."
The magazine said Fury's defeat of Klitschko "turned boxing's traditional glamour division upside down".
Following his title win in Dusseldorf, Fury caused controversy over derogatory remarks he made about women, and for criticising homosexuality and abortion.
Almost 140,000 people signed a petition calling for Fury to be removed from the BBC Sports Personality of the Year shortlist.
Fury remained on the list and, during the show in December, apologised if any of his comments "hurt anybody".
He finished fourth in the vote for the award, which was won by tennis player Andy Murray.
American former WBC, WBA and IBF title-holder Mike Tyson said about Fury: "He is the best heavyweight champion of the world since myself. He is the man, I don't care what anybody says.
"I know this is going to sound ignorant, he can say what he wants to say. You know who is going to look up to him? The people who never thought they had a chance in their life."
Former world welterweight and light-welterweight champion Ricky Hatton, in 2005, is the only other Briton to win the Ring award.
The Ring magazine has named world heavyweight champion Tyson Fury as its 2015 fighter of the year.