The move was part of an agreement brokered earlier this month at a summit of the leaders of Ukraine, Russia, Germany and France.
A rebel government official and the Ukrainian president's office confirmed that the swap has started.
In total, 142 prisoners were expected to be exchanged at a checkpoint near Horlivka in eastern Ukraine — 55 released by the rebels and 87 by Ukraine.
The last major prisoner swap between separatist rebels and Ukrainian forces took place in December 2017, with 233 rebels exchanged for 73 Ukrainians.
The fighting in eastern Ukraine since 2014 has killed more than 14,000 people. The conflict began about two months after Ukraine's Russia-friendly president fled the country amid massive protests in Kyiv. Russia's annexation of the Crimean Peninsula soon followed.
Hopes for ending the conflict have risen since the spring election of Ukrainian President Volodymyr Zelenskiy, who has been more amenable to negotiations with Russia on ending the war.
But prospects for peace are still troubled by questions over allowing local elections that would ensure the rebel regions more autonomy and about Ukraine regaining control of its border with Russia in the rebel areas.