The WNBA player was released last week in a prisoner swap for the notorious Russian arms dealer Viktor Bout.
She spoke for the first time since the exchange on Friday, thanking President Joe Biden and vowing to return for Phoenix Mercury this season.
“It feels so good to be home,” she said in a statement on Instagram.
“The last 10 months have been a battle at every turn. I dug deep to keep my faith and it was the love from so many of you that helped keep me going.”
“I also want to make one thing very clear: I intend to play basketball for the WNBA’s Phoenix Mercury this season,” Griner said.
The two-time Olympic gold medallist said she had departed Brooke Army Medical Center in San Antonio, Texas, where she spent a week recovering after landing in the US.
Griner also pledged to use her platform to help Biden secure the release of Paul Whelan, an ex-marine who has been in Russian custody for nearly four years on charges of spying.
The Biden administration faced criticism for failing to include Whelan in the Griner-Bout prisoner swap. The US said it had the choice of bringing home Griner or no one.
Biden is “committed to bringing Paul Whelan and all Americans home”, Griner said, urging “everyone that played a part in bringing me home to continue their efforts” to secure his release.
“Every family deserves to be whole,” she said.
Griner was arrested at a Moscow airport in February for possessing cannabis oil and later sent to a penal colony.
She spent 10 months in Russian custody before the US government – under pressure from activists, politicians and those close to Griner – struck a deal with Russia to release her for Bout, who was flown back after 12 years in US custody.
The elaborate swap involved two private planes bringing the pair to Abu Dhabi airport from Moscow and Washington, and then flying them home.
Griner, 32, is one of the best-known sportswomen in America. During the US basketball season the double Olympic champion is a star centre for Phoenix Mercury in the WNBA.
Her agent recently said the star had played basketball for the first time since her arrest during her stay at the US army post in Texas.
Her first move was a dunk, Lindsay Kagawa Colas told ESPN.