Detectives searching for French national Xavier Thomas, 45, recovered a body from the Thames near Limehouse.
Scotland Yard said Mr Thomas’ next of kin have been informed.
Mr Thomas, 45, is thought to have been struck by the terrorists' van on the bridge and witnesses reported him being thrown into the water during the London terror attack, which left his girlfriend Christine Delcros seriously injured.
Formal identification has not yet taken place, however Mr Thomas' next of kin have been informed of this development
Met Police said in a statement: “On Tuesday, 6 June at approximately 7.44pm the body of a man was recovered from the river, near Limehouse, by specialist officers from the Marine Police Unit.
“Formal identification has not yet taken place, however Mr Thomas' next of kin have been informed of this development.”
The French couple, who were visiting London for the weekend, were walking south over London Bridge around the time the attack started, according to police.
Detectives searching for French national Xavier Thomas pulled a body from the River Thames
Ms Delcros was seriously injured when she was struck by the van, while witnesses accounts suggest Mr Thomas was thrown into the River Thames by the impact.
Nathalie Cros Brohan said on Facebook on Monday that her sister, Ms Delcros, had been taken to hospital.
Three French citizens were among the eight people killed when terrorists drove a van into pedestrians and then went on a stabbing spree in Borough Market on Saturday.
Kirsty Boden, Christine Archibald, James McMullan and Sara Zelenak have been named as some of the people who were killed in the attack.
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South Australian nurse Kirsty Boden, 28, died after running to help people on London Bridge
Canadian Christine Archibald, 30, died after she was hit by the terrorists’ speeding van
South Australian nurse Kirsty Boden, 28, had been working at Guy's Hospital in London.
She died after running to help people on the London Bridge.
Her family said: "She was the most outgoing, kind and generous person who loved to help people.
“As she ran towards danger, in an effort to help people on the bridge, Kirsty sadly lost her life.
“We are so proud of Kirsty's brave actions, which demonstrate how selfless, caring and heroic she was, not only on that night, but throughout all of her life.
Sadiq Khan leads sombre vigil for London terror victims Tue, June 6, 2017
London Mayor Sadiq Khan lead a vigil to commemorate the victims of the London Bridge terror attack. Hundreds attended the event outside London's City Hall
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London Mayor Sadiq Khan bows his head
“Helping people was what she loved to do in her job as a nurse and in her daily life.”
Canadian Christine Archibald, 30, died after she was hit by the terrorists’ speeding van on London Bridge.
Writing on Facebook, Cassie Ferguson Rowe said her younger brother Tyler Ferguson held his fiancée Christine in his arms after the attack.
Ms Archibald's family said in a statement: "We grieve the loss of our beautiful, loving daughter and sister. She had room in her heart for everyone and believed strongly that every person was to be valued and respected.
"She lived this belief, working in a shelter for the homeless until she moved to Europe to be with her fiancé.
"She would have had no understanding of the callous cruelty that caused her death.”
James McMullan, 32, from Hackney was killed outside the Barrowboy And Banker pub
Spanish banker Ignacio Echeverria died after fending off a terrorist and helping an injured woman
James McMullan, 32, from Hackney, was last seen outside the Barrowboy And Banker pub and his sister said police have told her his bank card was found on a body at the scene of the attack.
Melissa McMullan told Sky News "While our pain will never diminish, it is important for us all to carry on with our lives in direct opposition to those who wish to destroy us and remember that hatred is the refuge of small-minded individuals and will only breed more.
Alexandre Pigeard, 27, has been named by French media as one of those killed.
Brittany news outlet Le Telegramme reported an account from Boro Bistro manager Vincent Le Berre, who told how his colleague, Mr Pigeard, was attacked by a terrorist in the bar near Borough Market on Saturday night.
Mr Le Berre said: "I managed to escape him, but my friend Alexandre did not have that chance. He was hit in the neck with a knife."
According to French media, Mr Pigeard was from Caen, in Normandy, but had been living in London for more than two years.
French chef Sebastien Belanger, 36, is thought to be among those who died.
He was drinking at the Boro Bistro near Borough Market when the area came under attack.
Originally from Angers, western France, Mr Belanger had lived in London for several years and worked at the Coq d'Argent restaurant in the City, the Daily Telegraph reported.
Family and friends of Australian Sara Zelenak have said she died in the attack as they posted tributes to her online.
Her father, Mark Wallace, shared a video of his daughter and wrote: "I really miss that funny little laugh."
London Bridge terror: Scenes as armed police respond Sun, June 4, 2017
At least two people have died after being after reportedly being struck by a van on London Bridge on Saturday night.
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Armed police responding to the incident at London Bridge
Friend Elle Bishop said on Facebook: "I find solace in the fact that the hate that saw you taken from us, you have never felt inside, making you a remarkable young woman."
Ms Zelenak has not been seen since the attack after she became separated from friends on Saturday night.
The family of Spanish banker Ignacio Echeverria have confirmed he was killed in the London Bridge attack after trying to fend off a terrorist with his skateboard and help an injured woman.
According to Spanish media, relatives were told of the 39-year-old's death by Spanish ambassador Carlos Bastarreche, after the family flew in to London on Tuesday.
Mr Echeverria was reported missing after he was last seen in the area of Borough Market defending a woman with his skateboard.
The terror investigation into Saturday’s attack continues with detectives carrying out a search warrant at an address in east London in the early hours of this morning.
Officers from the Met's Counter Terrorism Command, supported by officers from the Territorial Support Group, entered the address in Ilford at around 1.30am.
A 30-year-old man was arrested on suspicion of the commission, preparation or instigation of terrorist acts (contrary to section 5 Terrorism Act 2006) and has been taken into custody at a south London police station under the Terrorism Act 2000.
It comes as parts of Borough reopen to the public.
A large part of the outer cordon of the crime scene in place following the terrorist attack in London Bridge has now been reopened.
Borough High Street and the roads and area east of the High Street have now reopened to the public. Borough Market and a small surrounding area remain closed.
Any members of the public who urgently require temporary access to the remaining crime scene should present themselves to the mobile station positioned on Southwark Street junction with Redcross Way with identification to discuss their requirements and if appropriate will be escorted in and out of the scene.