Twelve FDNY units and 60 fire personnel responded to the scene at the Amsterdam Avenue apartment complex just before 3 a.m. Tuesday.
Firefighters searched the 13-story building, part of the city-run Amsterdam Houses, after residents reported smoke.
The victim was found in a fifth floor apartment.
The resident, a man believed to be in his 50s, was reported in critical condition and rushed to Mount Sinai West Hospital, where he was pronounced dead.
A firefighter was treated for a minor injury.
The cause of the fire is under investigation.
Ex-Brit turned Manhattan resident since 2008.