Should Fury overcome the former cruiserweight champion, then he would be just one fight away from a clash 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," Fury told Eurosport.
"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 has not lost in 20 professional fights.