The London Bridge attack is the third in Britain this year, following a vehicle and knife rampage near Parliament in March, which killed five, and the May 22 bombing at an Ariana Grande concert in Manchester in which 22 people died.
The force said formal identification has not yet taken place, but Xavier Thomas's next of kin had been informed.
Eight people were killed and dozens were injured.
The raids by detectives from the Metropolitan Police's Counter Terrorism Command, supported by armed police, are not connected to the London Bridge attack, Scotland Yard said.
Of the eight people killed, British authorities have publicly identified two Australian nationals: Kirsty Boden, as confirmed Tuesday by NHS England, and Sara Zelenak, as confirmed Wednesday by police.
The body was found late last night about two kilometres downstream from London Bridge, where Saturday's truck-ramming and knife attacks began.
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Thomas, who was visiting London for the weekend with his girlfriend, has not been seen since Saturday's assault which was claimed by the ISIS. Early accounts suggest Thomas was thrown into the river.
His girlfriend was struck by the van and seriously injured. Police arrested a 27-year-old man in connection with the attack on Monday and released 12 others without charges, officials said. He was known to security services and even featured in a television documentary entitled "The Jihadis Next Door". Ireland's national broadcaster RTE reported that Redouane had an Irish residency card and had lived in Dublin.
The families of the London attackers have condemned their actions on Wednesday, with relatives of Khuram Butt, Youssef Zaghba and the ex-partner of Rachid Redouane saying they were shocked at what had happened.
Hours after it was published, police made three more arrests.
He said Zaghba was always tracked by Italian intelligence officers while in the country and that United Kingdom authorities were informed.
Security measures were heightened on Thursday as millions headed out to vote in the general election.
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