Aiden Aslin, 28, from Nottinghamshire, Shaun Pinner, 48, from Bedfordshire, were charged with being foreign mercenaries having been captured in the southern city of Mariupol.
A third man, Moroccan national Saaudun Brahim, has also been given the death penalty.
They were sentenced in a court in the Donetsk People's Republic, which is not internationally recognised.
Foreign secretary Liz Truss condemned the death sentences handed to Mr Aslin and Mr Pinner as a “sham judgment with absolutely no legitimacy”.
She tweeted: "I utterly condemn the sentencing of Aiden Aslin and Shaun Pinner held by Russian proxies in eastern Ukraine.
"They are prisoners of war. This is a sham judgment with absolutely no legitimacy.
"My thoughts are with the families. We continue to do everything we can to support them.
Downing Street also said they were "deeply concerned" about the situation.
Mr Aslin joined the Ukrainian marines in 2018 and had been fighting with his unit in Mariupol during the Ukraine crisis.
In April, he was captured after his unit was surrounded and they ran out of ammunition and supplies.
Russia claims he is a foreign mercenary — which would prevent him from having protection under the Geneva Convention — when, in fact, Mr Aslin holds dual citizenship and was fighting with the Ukrainian army.
The Russian state news agency said Mr Pinner and Mr Brahim had pleaded guilty to actions aimed at the violent seizure of power.
All three face death by firing squad. They have a month to appeal.
A video shared by Russian media appeared to show Mr Aslin pleading guilty to a lesser charge involving weapons and explosives.
He was seen standing in the cage and leafing through a sheaf of legal documents as the charge was translated to him.
Before they were sentenced the Foreign, Commonwealth and Development Office condemned what it called the exploitation of prisoners of war for political purposes.
"They are entitled to combatant immunity and should not be prosecuted for participation in hostilities," said a spokesperson late on Wednesday.
The UK government has said Mr Aslin was a full member of the Ukrainian armed forces, which guarantee him certain prisoner of war protections.
Russia has accused Mr Aslin of being a mercenary, which is relatively unprotected under prisoner of war laws.
Mr Aslin's family have been trying to get him released for weeks.
His brother Nathan Wood said in April he is confident Mr Aslin will be released but feared it “could all take days, weeks, months”.
Ukraine has also begun prosecuting captured Russian troops.
Last month Vadim Shishimarin, 21, was convicted of war crimes after he admitted shooting and killing a 62-year-old civilian.
Russia denies committing any war crimes but Ukraine says it is investigating 13,000 different accusations.