It said seven officers and 88 soldiers and sergeants were freed, and most had been in captivity since 2022.
The committee posted a video showing Ukrainian troops boarding buses to be transported home and cheering.
It showed one serviceman, wrapped in the blue and yellow Ukrainian flag, saying into his mobile phone: “I still cannot believe that I am at home.”
Twenty-three people had taken part in the three-month defence of the Sea of Azov port of Mariupol, and were captured by Russian forces in May 2022, the committee said.
“Many returning Ukrainian soldiers suffer from consequences of their wounds and have chronic diseases that require long-term treatment,” the panel said on Telegram.
In the second exchange in June, Russia and Ukraine each handed back 90 prisoners.