Planes arrived at the Russian and Ukrainian capitals to collect inmates on Saturday, according to Russian Interfax news agency and Flightradar data.
A government source in the Ukrainian capital Kiev also confirmed to the AFP news agency that the swap involving 35 prisoners from each side was taking place.
Russian state television earlier broadcast footage of buses leaving a jail in the capital, Moscow.
“Buses have left the Lefortovo jail within the framework of preparations for a prisoner exchange,” the Rossiya 24 news channel reported.
The head of the defence team of which 24 Ukrainian sailors captured by Russia in November in the Sea of Azov told AFP they would be part of the swap.
“According to my information, they were put on a bus. All 24 of them,” Nikolai Polozov said, adding that he expected them to arrive in Ukraine “in the next few hours”.
A view shows a Russian plane ahead of a prisoner exchange between Russia and Ukraine, at Boryspil International Airport outside Kiev [Gleb Garanich/Reuters]
Attorney Mark Feigin tweeted before the development that the exchange was under way and that the prisoners from the Russian side included the 24 Ukrainian sailors.
He said the deal also included Ukrainian journalist Roman Sushchenko who he represented and filmmaker Oleg Sentsov, convicted of plotting “terrorist” acts.
If completed, it would be the first prisoner exchange between Russia and Ukraine since 2017.
The exchange could be a significant step towards easing Russia-Ukraine relations and may boost the chances of a resolution to the violence in Ukraine’s east.
Russia and Ukraine have been in a conflict since 2014 when Russia annexed Crimea after a controversial referendum.
Fighting between troops and Russia-backed separatists has killed more than 13,000 people since then.
Ukraine blames the Kremlin for separatist violence in eastern Ukraine.
Al Jazeera and news agencies