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.