She was expected to be transferred to a nearby military facility for medical checks, US media reported.
Griner was exchanged in Abu Dhabi on Thursday for Viktor Bout, a 55-year-old Russian national who was serving a 25-year sentence in a US prison.
In footage released by Russian state media, Griner, shorn of her distinctive dreadlocks, and a relaxed and animated Bout could be seen crossing paths on the airport tarmac and heading towards the planes that would take them home.
President Joe Biden said on Thursday that he had spoken to her and that she was in "good spirits" after suffering "needless trauma."
Griner, a two-time Olympic gold medalist, WNBA champion and LGBTQ trailblazer, was arrested at a Moscow airport against a backdrop of soaring tensions over Ukraine.
She was accused of possessing vape cartridges with a small quantity of cannabis oil and sentenced in August to nine years in prison.
Bout, who was accused of arming rebels in some of the world's bloodiest conflicts, was detained in a US sting operation in Thailand in 2008, extradited to the United States and sentenced in 2012 to 25 years behind bars.
He landed in Russia on Thursday, state television said. "Don't worry, everything is OK, I love you very much," he told his mother Raisa.
While Griner's family and friends celebrated her release, another American held in Russia, former US Marine Paul Whelan, detained since 2018 and accused of spying, was not part of Thursday's exchange.
He told CNN he was "greatly disappointed."
"I don't understand why I'm still sitting here," Whelan told CNN in a phone call from a Russian penal colony.
Biden pledged to obtain Whelan's freedom, saying "we will never give up."
"Sadly, for totally illegitimate reasons, Russia is treating Paul's case different than Brittney's," he said.
As for Griner's release, Biden said: "This is a day we've worked toward for a long time. It took painstaking and intense negotiations."
'Family is whole'
Biden announced Griner's release on Thursday flanked by her wife, Cherelle Griner, Vice President Kamala Harris and Secretary of State Antony Blinken.
"I'm just standing here, overwhelmed with emotions," Cherelle Griner said.
"Today my family is whole, but as you all are aware there's so many other families who are not whole."
The Griner family thanked President Biden and his administration in a statement, and said they "pray for Paul and for the swift and safe return of all wrongfully-detained Americans."
WNBA commissioner Cathy Engelbert said there was a "collective wave of joy and relief" in the women's professional league where Griner has been a star for a decade with the Phoenix Mercury.
Biden thanked the United Arab Emirates for helping "facilitate" Griner's release and the UAE issued a joint statement with Saudi Arabia saying it was the result of "mediation efforts" by leaders of the two Arab nations.
White House Press Secretary Karine Jean-Pierre said, however, there was "no mediation involved" and "the only countries that negotiated this deal were the United States and Russia."
'Rescue our compatriot'
At the time of her arrest, Griner had been playing for a professional team in Russia, as a number of WNBA players do in the off-season.
She pleaded guilty to the charges against her, but said she did not intend to break the law or use the banned substance in Russia.
Griner testified that she had permission from a US doctor to use medicinal cannabis to relieve pain from her many injuries.
The use of medical marijuana is not allowed in Russia.
The Russian foreign ministry said it had been negotiating with Washington to secure Bout's release "for a long time" and that initially the United States had "refused dialogue" on including him in any swap.
"Nevertheless, the Russian Federation continued to actively work to rescue our compatriot," it said.
The 2005 film "Lord of War" starring Nicolas Cage was based in part on Bout's arms trafficking, and he has been the subject of several books and TV shows.
Russia's ambassador to the United States, Anatoly Antonov, told Bout in a video message that he was aware that the arms dealer had been subjected to "powerful physical and moral pressure" while in prison, Russian news agency TASS reported.
Asked about Bout's release, a senior US defense official said "there is a concern that he would return to doing the same kind of work that he's done in the past."
Moscow said on Friday that ties with Washington remained in "crisis".
"It is probably wrong to draw any hypothetical conclusions that this could be a step towards overcoming the crisis that we currently have in bilateral relations," Kremlin spokesman Dmitry Peskov told the Izvestia newspaper.
Ties "continue to remain in a sad state."
© Agence France-Presse
