The Metropolitan Police said the body was found on Tuesday downstream from the bridge. The force says formal identification has not yet taken place, but Xavier Thomas' next of kin have been informed.
In a statement, police said the death toll in the vehicle and knife attack had risen to eight. Almost 50 were wounded.
Mr Thomas, 45, was walking with his girlfriend over the bridge when the attack began on Saturday night.
Police said earlier that witness accounts suggested he might have been thrown into the river. His girlfriend was struck and seriously injured by the van.