Ukrainian president Volodymyr Zelensky’s chief of staff confirmed that the bodies of Chris Parry, 28, and Andrew Bagshaw, 47, had been returned to Ukraine.
It is not yet known when they will be handed to British embassy staff to be returned home.
The two volunteers had last been seen heading to the city of Soledar on 6 January. The families of the men say they were killed while carrying out a humanitarian rescue. Mr Bagshaw’s family said the pair had been attempting to assist an elderly woman when their cars were hit by a shell.
Soledar has been a focus of intense fighting between Ukrainian and Russian forces. Russia’s military claimed to have captured the Ukrainian salt-mining town, calling the victory an “important” step for its offensive. The claim of victory was disputed by Ukrainian government officials in Kyiv.
Ukraine’s chief of staff Andriy Yermak said 116 Ukrainian soldiers had been released on Saturday, despite the continued fighting between the two sides. Mr Yermak said that the prisoners who had been returned included defenders of Mariupol, partisans from Kherson, and snipers from Bakhmut, as well as two personnel involved in special operations.
Russia’s defence ministry said that 63 of its servicemen had been returned in what was described as a “complex mediation process”. The defence ministry said the group included personnel in a “sensitive category” thanks to mediation involving the United Arab Emirates, although no further details were given of the roles of those released.
In a statement released by the UK Foreign Office, Mr Parry’s family said they were “extremely proud” of his “selfless determination in helping the old, young and disadvantaged” in Ukraine.
They said: “We never imagined we would be saying goodbye to Chris when he had such a full life ahead of him. He was a caring son, fantastic brother, a best friend to so many and a loving partner to Olga.”
They praised Mr Parry, originally from Truro in Cornwall, who they said had “found himself drawn to Ukraine in March in its darkest hour at the start of the Russian invasion and helped those most in need, saving over 400 lives plus many abandoned animals”.
In a statement, Mr Bagshaw’s family said last month: “Andrew selflessly took many personal risks and saved many lives; we love him and are very proud indeed of what he did.
“The world needs to be strong and stand with Ukraine, giving them the military support they need now, and help to rebuild their shattered country after the war.”
It comes as prime minister Rishi Sunak told president Volodymyr Zelensky that he is determined to ensure Britain's promised military aid reaches Ukraine as quicky as possible.
In a call on Saturday, he said that Ukrainian troops in the UK have begun training this week on Challenger 2 main battle tanks, which Britain has agreed to supply to the government in Kyiv.
A Downing Street spokesman said: “Both leaders agreed that it was vital that international partners accelerated their assistance to Ukraine to help seize the opportunity to push Russian forces back, as well as looking at how they could support the long-term capability of Ukraine's armed forces.
“The greatest weapon in Ukraine's arsenal was the collective international unity in support of Ukraine, the leaders agreed.”