British police said that they had recovered a body from the Thames river believed to be that of 45-year-old Frenchman Xavier Thomas, missing since the night of the attack.
"Xavier was in London for the weekend with his girlfriend. They were walking south over London Bridge at around the time the attack started," police said.
Thomas's girlfriend was seriously injured after being hit by the attackers' van.
The Metropolitan Police says the body was found on Tuesday downstream near Limehouse from the bridge.
Thomas's next of kin have been told, police said, but formal identification has not yet taken place.
Thomas was walking with his girlfriend over the bridge when the attack began on Saturday night.
Police said earlier that witness accounts suggested Thomas might have been thrown into the river.
Thomas' girlfriend was struck and seriously injured by the van.
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So far four of those killed in the attack have been named as Australian Kirsty Boden, Canadian national Chrissy Archibald, James McMullan, from Hackney, and French national Alexandre Pigeard.
Wednesday's announcement comes as UK authorities face new questions over how one of the London Bridge attackers was let into Britain despite being on a security watch list.
Youssef Zaghba had been flagged to British intelligence services after telling Italian police "I'm going to be a terrorist" when he was reportedly stopped trying to travel to Syria.
Italian prosecutor Giuseppe Amato said there was not enough evidence to arrest or charge the 22-year-old when he was caught at Bologna airport last year.
He said Zaghba was always tracked by Italian intelligence officers while in the country and that UK authorities were informed.
"We did everything we could have done, but there weren't elements of proof that he was a terrorist," he added.
The youngest of the attackers, an Italian national of Moroccan descent, he was allowed to enter the UK and had been living in east London.
Counter-terror agencies were already under intense scrutiny after it was revealed Khuram Shazad Butt, 27, and Rachid Redouane, 30, were also known to security services.
They drove into pedestrians on London Bridge before stabbing people in Borough Market on Saturday night.
