Thomas, 45, 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.
Relatives of Australian Sara Zelenak have confirmed she was killed in the London attacks over the weekend.
The 21-year-old worked as a nanny in London and had previously been described as missing after the attacks Saturday night.
Her aunt, Tara, says Zelenak's mother Julie Wallace broke down when she learned of her daughter's death while traveling to Britain.
Tara posted on Facebook: "Even though there was limbo for days, there was still a bit of hope."
Seven people were killed and dozens wounded in the attacks by three assailants near London Bridge. Another Australian who died, nurse Kirsty Boden, was said to have been trying to help other victims when she was killed.
A former U.S. intelligence official has offered his nation's condolences to three Australians killed in attacks in London and Melbourne, Australia.
Two Australians were among the seven killed in a van and knife attacks on and on Saturday. A Chinese-born Australian was killed by a gunman who was shot dead by police in what authorities described as a terrorist incident in Melbourne on Monday.
Former U.S. Director of National Intelligence Jim Clapper said in a speech to Australia's National Press Club: "Unfortunately, on a serious note, I am compelled to acknowledge the tragic loss of two Australian citizens in the mindless, heinous terrorist attack in London."
He added: "On behalf of the United States, I want to offer heartfelt condolences and prayers and similar thoughts go out to the family of the man killed in Melbourne."
Prince Harry has spoken in praise of Australians living in London after two of them were confirmed to have been killed in the van and knife attacks there over the weekend.
Harry said: "Australians form an important and vibrant part of the fabric of life in London and we are reminded of that in good times and bad." He said his heart went out to the victims, their friends and families.
Authorities have said Australian nurse Kirsty Boden was trying to help other victims when she was killed in the attacks Saturday night on London Bridge and in Borough Market. The identity of the second Australian among the seven dead has not been released.
Harry was in Sydney on Wednesday to launch the 2018 Invictus Games. He created the sporting competition for injured and sick servicemen and women after his two tours of duty in Afghanistan.