The White House said the US had negotiated the complex trade with Russia and other countries.
It said eight prisoners held in the United States and several European countries were being sent back to Russia.
Germany confirmed that they included Vadim Krasikov, convicted of murdering an exiled dissident in Berlin.
US President Joe Biden hailed the deal as "a feat of diplomacy and friendship" and praised allies for their "bold and brave decisions".
"This would not have been possible without our allies," he said, adding: "Today is a powerful example of why it's vital to have friends in this world."
Turkey, which co-ordinated the exchange, said 10 people, including two children, had been moved to Russia, 13 to Germany and three to the United States.
A Russian government plane believed to be carrying released prisoners left Turkey for Russia. (AP PHOTO)
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.
A Reuters reporter saw a Russian government aircraft taking off from Ankara.
Evan Gershkovich, Alsu Kurmasheva, Paul Whelan. Free. Amazing. — Paul Beckett (@paulwsj) #IStandWithEvan pic.twitter.com/mGtNjTwedBAugust 1, 2024
The Kremlin said Russia's decision to pardon and free prisoners had been made in order to bring Russian captives home.
Former Russian president Dmitry Medvedev, a vociferous backer of Russia's war in Ukraine, which has prompted the arrest of hundreds of critics and driven relations with the US to their worst level since the Cold War, was acerbic in a Telegram post: "Let the traitors now feverishly pick up new names and actively disguise themselves under witness protection programmes."
In the last major exchange in 2010, 14 prisoners were exchanged.
In December 2022, Russia traded US basketball star Brittney Griner, sentenced to nine years for having vape cartridges containing cannabis oil in her luggage, for arms dealer Viktor Bout, serving a 25-year sentence in the US.
Krasikov is a colonel in the Russian FSB security service who was serving a life sentence in Germany for murdering an exiled Chechen-Georgian dissident in a Berlin park.
Russian President Vladimir Putin himself had indicated he wanted Krasikov back and the German government, commenting on the swap deal, said it was "not an easy decision" to free him.
Rico Krieger, a German sentenced to death in Belarus on terrorism charges, was pardoned on Tuesday by President Alexander Lukashenko, a Putin ally, prior to being freed.
Also released was Vladimir Kara-Murza, a Russian-UK dissident serving 25 years for treason after telling the Arizona House of Representatives in March 2022 that Putin was bombing Ukrainian homes, hospitals and schools.
Freed along with him were human rights activist Oleg Orlov and Russian opposition politician Ilya Yashin.
The US has freed Russian citizen Vladislav Klyushin, convicted of wire fraud and securities fraud. (AP PHOTO)
Many of those freed had worked with Alexei Navalny, Russia's leading opposition figure, who died in unclear circumstances in an Arctic penal colony in February.
His widow Yulia Navalnaya, who has vowed to continue his work, hailed the releases as "a great happiness".
"Every released political prisoner is a huge victory and joy. No one should be held hostage by Putin, tortured and die in Putin's prison," she wrote on X.
The massive exchange comes in the waning months of Biden's term in office after he stood down from his re-election bid, nearly four years marked by a sharp increase in tensions between the countries over Russia's invasion of Ukraine.
Administration officials said the multi-country deal appeared to be a one-time exchange that does not herald an easing in tensions between the nuclear-armed countries.
Those released from the US were named as Roman Seleznev, Vladislav Klyushin and Vadim Konoshchenok.
Seleznev, the son of a Russian MP, was convicted in the US in 2017 of hacking into more than 500 businesses and stealing millions of credit card numbers.
Businessman Klyushin was convicted in Boston in 2023 of charges including wire fraud and securities fraud in a nearly $100 million scheme that relied on secret earnings information stolen via hacking US computer networks.
Konoshchenok was extradited to the US from Estonia last year to face charges he smuggled ammunition and dual-use technology to help Russia's war in Ukraine.
