The verdict from a panel of three judges read out in court said sergeant Aleksander Aleksandrov and captain Yevgeny Yerofeyev were guilty of participating in "an aggressive war" against Ukraine and committing "a terrorist attack".
Kiev insists that the duo were serving as members of an elite Russian military intelligence unit when they were captured in the pro-Moscow separatist region of Lugansk in May 2015.
Russia says both had resigned from active duty before crossing into the war zone of their own free will.
Aleksandrov and Yerofeyev stood impassively in a glass cage for defendants while the decision was read out, as journalists crowded into the cramped Kiev courtroom.
Many observers doubt that the Russian duo will serve their sentences in Ukraine as the verdict is seen as a potential step towards a much-anticipated prisoner exchange for Savchenko.
Ukrainian President Petro Poroshenko has proposed swapping the soldiers for the Kiev-born helicopter pilot who was in March sentenced to 22 years in prison by a Russian court for her alleged involvement in the killing of two Moscow reporters in the war zone.
Savchenko -- who has become a national hero at home -- began refusing all food and liquids in protest at her sentence on April 6 and her health is believed to be deteriorating rapidly.
The trial of Aleksandrov and Yerofeyev has driven yet another wedge between Moscow and Kiev, with the two sides locked in a bitter feud over Russia's 2014 annexation of Crimea and alleged responsibility for the war in east Ukraine that has left nearly 9,200 people dead.
Ukraine holds up the capture of the soldiers as further proof that Moscow deployed troops to fight alongside rebels despite the Kremlin's claims that it has not been directly involved in the conflict.
Kiev cites testimony the two men gave during their interrogation and in subsequent conversations with reporters in which both acknowledged to being active members of Russia's GRU military intelligence at the time.
They recanted those statements during the trial.
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