Griner arrived in the capital of Abu Dhabi by private plane from Moscow, as the Russian arms dealer she was being exchanged for, Viktor Bout, arrived on a private plane from Washington.
The two walked past each other on the tarmac, a US official said.
Her brutal 10-months in captivity ended after months of fruitless negotiations between the United States and Russia, complicated by Russia's invasion of Ukraine and the souring of U.S.-Russia relations.
A senior administration official said President Joe Biden personally tracked the negotiations closely for months, but it was only in recent weeks that he made the "very painful" decision to provide clemency to Bout to get the swap done.
The UAE president and Saudi crown prince led mediation efforts that secured Griner's release, a UAE-Saudi joint statement said.
This was later refuted by the US government, who said that they and Russia were the sole negotiators.
"The only countries that negotiated this deal were the United States and Russia," White House press secretary Karine Jean-Pierre said, when asked about Saudi Arabia's role. "There was no mediation involved."
Biden said on Thursday that he had spoken with Griner and she would be back in the United States within 24 hours.
Griner, a star of the Women's National Basketball Association's Phoenix Mercury, was arrested on February 17 at an airport outside Moscow for carrying vape cartridges containing hashish oil in her luggage.
She was subsequently convicted of drug smuggling and transferred to one of Russia's most feared penal colonies, where former inmates have described torture, harsh beatings and slave labor conditions.
During the prisoner exchange on Thursday, Griner was met on the tarmac in UAE by chief US hostage negotiator Roger Carstens. She was "all smiles and extremely grateful for all the efforts both USG (US government) and outside the government that has been put on to get her home," a U.S official said.
Bout's release leaves behind US Marine Paul Whelan in Russian custody, a situation his family called a "catastrophe."
"The negotiations ... focused on getting both Americans held wrongfully detained in Russia home," a U.S. official said. "Ultimately ... it became clear that the choice was, as I've emphasized, that it was bringing Brittney Griner home right now or bringing no American home right now."
Griner's wife, Cherelle, reacted to her release alongside US President Joe Biden.
"I am standing here overwhelmed with emotions, but the most important emotion I have right now is sincere gratitude for President Biden and his entire administration.
"Today, my family is whole, but there are so many other families who are not whole. (Griner) and I will remain committed to getting every American home."
