Buses from a Moscow prison believed to be carrying Ukrainian prisoners arrived at the capital's Vnukovo airport on Saturday.
A prisoner exchange could be a significant step toward easing Russia-Ukraine relations and raising chances for resolving the conflict in Ukraine's east where fighting between troops and Russia-backed separatists has killed more than 13,000 people since 2014.
Russian lawyer Mark Feigin, who defended a Ukrainian imprisoned for spying, tweeted to say that the exchange is underway.
He said that the prisoners from the Russian side include 24 Ukrainian sailors who were seized by Russia in November.
Mr Feigin also said they include Ukrainian journalist Roman Sushchenko, who he has represented, and filmmaker Oleg Sentsov, convicted of plotting terrorist acts.
Planes from each country have arrived at each other's capitals to collect inmates, flightradar data showed and Interfax reported.
Ukranian President Volodymyr Zelensky, who was elected in April, has previously said his top priority was to end the conflict with Russia.
While officials in Russia have said the prisoner exchange is vital for improving the "atmosphere surrounding a settlement of the Ukrainian crisis".
