Shaun Pinner, 48, from Bedfordshire has been sentenced to death according to Russian-owned news agency RIA Novosti.
Aiden Aslin, 28, from Nottinghamshire and another man - Moroccan national Saaudun Brahim - have also been sentenced to death it is being reported.
The hearing took place in a court in the Donetsk People's Republic, which is held by pro-Russian rebels.
The court is not internationally recognised.
Many observers deemed the case a “show trial”.
On Telegram RIA News said: "The Supreme Court of the DPR passed the first sentence on mercenaries- the British Aiden Aslin and Sean Pinner and the Moroccan Saadun Brahim were sentenced to death, RIA Novosti correspondent reports from the courtroom."
Pinner, an ex-British Army soldier originally from Bedfordshire, moved to Ukraine four years ago to join the Ukrainian military.
Pinner and his fellow Briton have said they were serving in the Ukrainian marines, making them active-duty soldiers who should be protected by the Geneva conventions on prisoners of war. However, the Russian state media has portrayed the men as mercenaries, and the court has convicted them on the charge of “being a mercenary”.
Both Britons were captured when their unit surrendered in Ukraine's port city of Mariupol as it came under a brutal siege by Russian forces.
MP Robert Jenrick told BBC Radio 4 that the trial was “a completely outrageous breach of international law and it should be condemned”.
He added: “The Russian authorities have chosen to make an example out of these two British nationals and it is, I think, completely shameful.”
Judge Alexander Nikulin said: 'The aggregated penalty for the crimes [means] the sentence Aiden Aslin to an exceptional measure of punishment, the death penalty.
'The aggregated penalty for the crimes [means] the sentence [of] Shaun Pinner to an exceptional measure of punishment, the death penalty.'
There is a moratorium on the death penalty in Russia, but not in the territory it occupies in eastern Ukraine.
Yesterday, Russian State TV claimed Boris Johnson's popularity will fall if British fighters are executed – despite the case still being ongoing.