Around 30 firefighters and five fire engines were called to Dorset Road just after midnight.
The fire was in a first-floor maisonette of an 11-storey residential block, where part of the flat was damaged.
Firefighters found a man inside the property, but he was declared dead at the scene.
Crews from Lambeth, Clapham, Peckham and Battersea fire stations attended.
The fire was brought under control by 1.27am.
The cause of the fire is being investigated by the London Fire Brigade and the Metropolitan Police.
