Aiden Aslin, 28, and Shaun Pinner, 48, were convicted of taking action towards violent seizure of power at a court in the self-proclaimed Donetsk People’s Republic.
The UK Government insisted the judgment had no legitimacy and the pair should be treated as prisoners of war.
Ms Truss said: “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.”
A No.10 spokesman said: “We are obviously deeply concerned by this. We have said continually that prisoners of war shouldn’t be exploited for political purposes.
“Under the Geneva Convention, prisoners of war are entitled to combatant immunity and they should not be prosecuted for participation in hostilities.
“So we will continue to work with the Ukrainian authorities to try to secure the release of any British nationals who were serving in the Ukrainian armed forces and who are being held as prisoners of war.”
A third man, Moroccan national Saaudun Brahim, was convicted alongside Mr Aslin and Mr Pinner.
The men were accused of being “mercenaries” after fighting with Ukrainian troops.
Russian media outlet RIA Novosti reported the three are set to face a firing squad.
Interfax, a Russian news agency, claimed the men would be able to appeal against their convictions.
Mr Aslin, originally from Newark-on-Trent in Nottinghamshire, and Mr Pinner were both members of regular Ukrainian military units fighting in Mariupol, the southern port city that was the scene of some of the heaviest fighting since Vladimir Putin’s invasion of Ukraine.
Tory former minister Robert Jenrick, who represents the Newark constituency where Mr Aslin lived, called for the Russian ambassador to the UK to be summoned to the Foreign Office.
He said: “This disgusting Soviet-era style show trial is the latest reminder of the depravity of Putin’s regime.
“Russia should be clear, they cannot treat British citizens like this and get away with it.
“Contrary to the Kremlin’s propaganda, Aiden Aslin is not a mercenary. He has been living in Ukraine and serving in its armed forces before Russia’s illegal invasion and as a prisoner of war is entitled to protection under the Geneva Convention.
“The Russian ambassador should be summoned to the Foreign Office to account for this most egregious breach of the Geneva Convention.
“Aiden must be released as soon as practicable.”
Shadow Europe minister Stephen Doughty said: “It is an outrageous and shameful breach of international law for the Russian regime or its puppets to use an illegitimate court to prosecute legitimate prisoners of war who are entitled to combatant immunity.”
There is a moratorium on the death penalty in Russia, but not in the territory it occupies in eastern Ukraine.
On Wednesday Russian State TV claimed Boris Johnson's popularity would fall if British fighters are executed – despite the case still being ongoing.