Jailed US Wall Street Journal reporter Evan Gershkovich and ex-US Marine Paul Whelan were among two dozen detainees from the United States, Russia and a number of their allies freed on Thursday in the biggest prisoner exchange since the Cold War.
The White House said the US had negotiated the complex trade with Russia and other countries. It said eight prisoners held in the West were being sent back to Russia.
Germany confirmed that they included Vadim Krasikov, convicted of murdering an exiled dissident in Berlin.
Turkey, which coordinated the exchange, said 10 prisoners, including two minors, had been moved to Russia, 13 to Germany and three to the United States. Also involved in the swap were Poland, Slovenia, Norway and Belarus.
"After the completion of the ratification procedures of the parties, the health checks ... the prisoners were placed on the planes of the countries to which they would be travelling with the approval and instructions of the MIT," the National Intelligence Agency (MIT) said in a statement.
It said it had authorised the return of the aircraft.
Kremlin spokesman Dmitry Peskov did not specifically confirm a swap but was quoted by the state news agency TASS as saying that, in principle, "all our enemies should stay there (abroad), and all those who are not our enemies should return".
In the last major exchange in 2010, 14 prisoners were exchanged.
Negotiated in secret for more than a year, the deal represents a major accomplishment for the parties and will be presented by the Biden administration as a marquee foreign policy success as the US presidential race enters its final months.

US peace envoys meet Zelenskyy in Kyiv after Putin talks
US targets three Iranian oil vessels after attack on Navy ships
Four killed in Israeli strikes on southern Lebanon
Indonesia's Anak Krakatau eruption halts flights, schools, fishing
Putin says US-Russia contacts beneficial as talks begin with Witkoff and Kushner
Chinese national rescued from Nepal tunnel 10 days after flash flood
US envoys Witkoff, Kushner arrive in Moscow for talks on peace in Ukraine
One dead, 11 people missing after mudslide in China's Jiangxi province
