But Kremlin spokesman Dmitry Peskov played down the suggestion by US President Donald Trump that the deal could make a significant contribution towards ending the Russia-Ukraine war.
Peskov said the freed Russian would return home in the coming days, and would not be named until they were back on Russian soil.
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.
The deal was the first that Russia has struck with Trump's new administration since he returned to the White House on January 20 for a second non-consecutive term.
Trump said it "could be a big important part" of ending the three-year-old Ukraine war.
Asked about that comment, 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."
Trump and Russian President Vladimir Putin have both said they are keen to meet to discuss Trump's ideas for bringing a swift conclusion to the war but no date for any summit has been announced.
US National Security Adviser Mike Waltz said Fogel was freed in a negotiated exchange "that serves as a show of good faith from the Russians and a sign we are moving in the right direction to end the brutal and terrible war in Ukraine".
Trump had said another person would be released on Wednesday, without identifying who it would be.
He called the terms of Fogel's release "very fair".
"We were treated very nicely by Russia. Actually, I hope that's the beginning of a relationship where we can end that (Ukraine) war and millions of people can stop being killed," Trump said.
Peskov declined to comment on the possibility of a further release.
Fogel was released into the custody of US Middle East envoy Steve Witkoff, who made an unannounced stop in Moscow on Tuesday to pick him up.
The Washington Post said that according to Fox News broadcaster Sean Hannity, Witkoff, a real estate developer and longtime friend of Trump, had a three-and-a-half hour meeting with Putin.
Peskov said he had "nothing to say" on that.
Asked what the United States gave up in exchange for Fogel, Trump told reporters earlier "not much" and called the release a show of good faith from the Russian side.
Russia's rouble rose against the US dollar on Wednesday on news of the Fogel deal and optimism about prospects for an easing of the Ukraine crisis.
