The Kremlin said the deal - the first it has struck with the new administration of US President Donald Trump - could help build trust between the two countries.
But it played down Trump's suggestion that the agreement could make a significant contribution towards ending the Russia-Ukraine war, which he has pledged to bring to a swift conclusion.
Alexander Vinnik was arrested in Greece in 2017 and extradited eventually to the US, where he pleaded guilty in May 2024 to conspiracy to commit money laundering.
He operated a cryptocurrency exchange, BTC-e, through which he was suspected of funnelling $US4 billion ($A6.4 billion) in proceeds from ransomware attacks, identity theft, drug rings and other criminal activity.
A US administration official confirmed to Reuters that he was being released but did not elaborate on the details or timing.
Earlier, the Kremlin said a Russian man was being freed but that it would not name him until he was back in the country.
Fogel, 63, was serving a 14-year sentence for drug smuggling after being caught at a Moscow airport with a small amount of marijuana.
He was flown on Tuesday to Washington DC, where he celebrated his release with Trump at the White House.
Trump said the deal "could be a big important part" of ending the three-year-old Ukraine war.
Asked about that comment, Kremlin spokesman Dmitry Peskov said any agreement on releasing prisoners was the result of "very, very meticulous negotiating work".
He added: "Of course, such agreements are hardly capable of becoming a breakthrough moment but at the same time, bit by bit, these are steps to build mutual trust, which is now at its lowest point."
A source close to the negotiations told Reuters that Saudi Crown Prince Mohammed bin Salman and Russia's sovereign wealth fund chief Kirill Dmitriev were involved in arranging the exchange.
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