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.

Major international artists include Hermann Nitsch, Melvin Moti, Dieter Roth and Rachel Mayeri.
There are new commissions from Susan Philipsz, Andrew Miller, Emily Speed, Kevin Harman and Anthony Schrag.
There are also retrospectives of acclaimed artists such as Ian Hamilton Finlay, Leslie Hunter and John Bellany.
Scots-born sound artist Philipsz, who won the Turner prize in 2010, will bring Timelines to the capital - a multi-site installation, developed in response to one of Edinburgh's famous One O'Clock Gun.
The gun is fired every day, except Sunday, from Edinburgh castle.
Philipsz's voice will call out each day in response to the firing of the gun, creating a domino effect as speakers sound along the timeline from Calton Hill to Edinburgh Castle.
Other new commissions include a pavilion made from salvaged materials and artworks made from rubble in skips.
As well as the commissions, the festival will feature new exhibitions by international artists such as Rachel Mayeri.
The Los Angeles-based artist collaborated with comparative psychologist Dr Sarah-Jane Vick to develop Primate Cinema: Apes as family.
It is a two-screen video installation that presents a drama written for chimpanzees and performed by human actors alongside the reactions of an audience of chimps.
It was researched and partly filmed at Edinburgh Zoo.
Dutch artist Melvin Moti is holding his first UK solo show, at the National Museums of Scotland.
One Thousand Points of Light features a new film focusing on light-reactive minerals and objects the artist has chosen from National Museums of Scotland's collections, ranging from fluorescing fossils to a glowing jellyfish.
There will also be several "summer blockbuster" exhibitions, with one exploring Picasso's lifelong connections with Britain, at the Scottish National Gallery of Modern Art.  Another major exhibition will feature the work of Van Gogh and Kandinsky, at the Scottish National Gallery.
As well as the major artists, there is an exhibition by TV presenter Harry Hill, who will also be performing during the Fringe, entitled My Hobby.
Edinburgh Art Festival was founded in 2004 and will run until 2 September.
The Ring magazine has named world heavyweight champion Tyson Fury as its 2015 fighter of the year.
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Edinburgh's art festival has begun its "most ambitious" programme yet, with 45 exhibitions showing in 30 of the city's museums and galleries during August.