South Wales Police was called to the area at about 08:00 GMT on Tuesday.
Police said the man was Lee Turner, 45, from Plasmarl, Swansea, who has been missing since 7 November.
A force spokesman said Mr Turner's family had been informed and his death was not being treated as suspicious. The circumstances of his death will be investigated on behalf of the coroner.
The body which was recovered from the water at Swansea Marina has been identified as a missing fisherman.