Griner was flown to the city of San Antonio and after reuniting with her family will have a medical checkup after her time in a Russian penal colony.
The actual exchange took place in the United Arab Emirates, where Griner and Bout crossed paths on the runway, heading to their flights home.
U.S. President Joe Biden, who had long pressed the Russian government to free Griner, officially announced her release Thursday.
"She represents the best of America," Biden said at the White House, noting that Griner would be back in the United States within 24 hours.
"I spoke with Brittney Griner," Biden said. "After months of being unjustly detained in Russia, held under intolerable circumstances. Brittney will soon be back in the arms of her loved ones, and she should have been there all along."
Griner's wife, Cherelle Griner, thanked Biden and an array of U.S. officials for their efforts in freeing her spouse after nine months of imprisonment. Cherelle Griner said that she and Brittney Griner would continue their support for the release of Paul Whelan, another American held in Russia who was not included in Thursday's deal.
Secretary of State Antony Blinken told a news conference, "This was not a choice of which American to bring home. The choice was one or none. I wish we could have brought Paul Whelan on the same plane as Brittney ..."
Earlier this year, Blinken and Russian Foreign Minister Sergey Lavrov talked about the would-be prisoner exchange, which at the time was their first known contact in more than five months, as Moscow's attacks on Ukraine continued.
In an extraordinary move during otherwise secret negotiations, Blinken revealed publicly in July that the U.S. had made a "substantial proposal" to Russia for Griner and Whelan.
In the end, Whelan, a 52-year-old Michigan corporate security executive imprisoned in Russia since December 2018 on espionage charges that his family and the U.S. government has said are baseless, was left out of the deal.
"Sadly, and for totally illegitimate reasons, Russia is treating Paul's case differently than Brittney's," Biden said. "And while we have not yet succeeded in securing Paul's release, we are not giving up. We will never give up."
Biden told Whelan's family, "We will keep negotiating in good faith. I guarantee it."
Bout, 55, had served 15 years of a 26-year prison sentence in the U.S. and was once nicknamed "the Merchant of Death." The Kremlin had long sought his release.
Bout is a former Soviet military translator turned international arms dealer. He was imprisoned for more than a decade after he was lured to Thailand in a U.S. Drug Enforcement Administration sting operation that spanned three continents.
(Some material in this report came from Agence France-Press and The Associated Press.)