By Steve Holland and Jeff Mason

WASHINGTON (Reuters) - Russia released American schoolteacher Marc Fogel on Tuesday following an unannounced visit to Moscow by U.S. special envoy Steve Witkoff and he was headed for a White House welcome, U.S. President Donald Trump said.

The release of 63-year-old Fogel, who had been detained in Russia since August 2021 and was serving a 14-year sentence, came as Trump seeks to improve relations with Moscow as part of an effort to secure an end to the war in Ukraine.

Trump told reporters that Fogel would visit the White House on his return to the U.S. late on Tuesday, and White House national security adviser Mike Waltz said he would also be reunited Tuesday night with his family, who celebrated the news.

On a plane home, Fogel, who is from Pennsylvania, was shown with a raised glass, a cheese plate and his U.S. passport in a photo posted on social media by Trump's chief hostage envoy Adam Boehler.

Asked what the United States gave up in exchange for Fogel, Trump said: "Not much" and called the release a show of good faith from the Russians.

"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.

Fogel was sentenced to 14 years in prison for drug smuggling after he was detained in Moscow's Sheremetyevo airport in August 2021 with 17 grams of marijuana - which he said was for medical use - in his luggage.

“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 Fogel family said in a statement.

"This has been the darkest and most painful period of our lives, but today, we begin to heal."

Fogel's Russian lawyer Dmitry Ovsyannikov confirmed the release to state news agency RIA.

"For the moment, we don't know on what grounds he was released from where he was serving time -- a pardon or something else," Ovsyannikov told TASS.

He told Russia's Interfax news agency that Fogel was last week transferred from a prison in Rybinsk, north of Moscow, to a pre-trial detention center in Moscow ahead of his release.

Fogel was left out of a historic swap of prisoners in August that involved 24 prisoners - 16 sent from Russia to the West, including Wall Street Journal reporter Evan Gershkovich, and eight sent back to Russia from the West.

Trump has indicated he has spoken with Russian President Vladimir Putin but has been vague on the details other than to say he is insistent on ending the three-year-old Ukraine war.

"We're making good progress there. I think, I really think we're making some very good progress," Trump told reporters about Ukraine on Tuesday.

(Reporting By Steve Holland; Additional reporting by Ron Popeski; Editing by Cynthia Osterman, Nick Zieminski and Don Durfee)