The 6'9" Fury, who is unbeaten in his 20 professional fights, will face former cruiserweight champion Cunningham at Madison Square Garden in what will be an IBF heavyweight eliminator for the number two contender spot.
Should Fury win, he would then be one fight away from a mandatory bout against current IBF champion Wladimir Klitschko.
"Cunningham's got all the tools; a former World Champion, good fighter, he's got a lot of skill. I'm looking to put on a devastating performance; the best of my career to date.” said Fury.
"I'm absolutely ecstatic to be fighting at Madison Square Garden; it goes back in history and I can't wait to put my name with a long list of champions who have fought there - I'm a historian of boxing myself so this is definitely the pinnacle of my career so far."
Fury was British and Commonwealth champion until last year, when he vacated the titles in order to work towards a world title bout. His last fight was a WBC eliminator in December against Kevin Johnson.