US national security adviser Mike Waltz said: "President Trump, Steve Witkoff and the president's advisers negotiated an exchange that serves as a show of good faith from the Russians".
Mr Fogel left Russia with Middle East envoy Steve Witkoff in what officials said could help bring about talks to end the Ukraine war.
"We are beyond grateful, relieved, and overwhelmed that after more than three years of detention, our father, husband, and son, Marc Fogel, is finally coming home," the family said in a statement.
"By tonight, Marc Fogel will be on American soil and reunited with his family and loved ones thanks to President Trump's leadership," he added.
Marc Fogel, 63, was pictured on a flight to the US on Tuesday - more than three years after he was arrested in Moscow for drug smuggling.
