The heavyweight scrapper said that he is "ecstatic" to be fighting at Madison Square Garden and promised fans a "devastating" show.
"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," ESPN quotes him as saying.
"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's promoter Mick Hennessy added: "I'm very proud to say that Tyson Fury's American debut is taking place at Madison Square Garden, New York. This is a dream debut in the US for Tyson."
Fury will be two fights away from an IBF Heavyweight title shot against champion Wladimir Klitschko if he defeats Cunningham.