"It is important that there are exchanges and that our people are returning home," Ukrainian President Volodymyr Zelenskiy said in a post on Telegram.
His chief of staff, Kyrylo Budanov, and Russia's defence ministry said the US and the UAE had assisted with the exchange.
Russia and Ukraine have conducted many prisoner swaps over four years of war, exchanging thousands of captives in total.
Zelenskiy said some of the returned captives, who included soldiers, border guards and police, had injuries while others had faced criminal charges in Russia.
In Ukraine, returning captives streamed off buses, many draped in their country's flag and overwhelmed with emotion.
"It still hasn't sunk in that I'm home, I was in captivity for three years ... our Ukrainian sky, our trees - this is happiness," said Serhiy, a soldier, who gave only his first name.
The Russian Ministry of Defence stated that the released Russian soldiers were still in Belarus, where the exchange had taken place.
Most recently, the warring parties had each released 500 prisoners at the beginning of March.
Russia has been waging war against neighbouring Ukraine for more than four years.
with DPA
