“She’s safe, she’s on a plane, she’s on her way home,” he said.
The deal, the second such exchange in eight months with Russia, has procured the release of the most prominent American detained abroad.
Griner is a two-time Olympic gold medalist whose months-long imprisonment on drug charges brought unprecedented attention to the population of wrongful detainees.
Mr Biden’s authorisation to release a Russian criminal once nicknamed “the Merchant of Death” underscored the escalating pressure his administration faced to get Griner home.
The swap took place at the Abu Dhabi airport in the United Arab Emirates, Russian news agencies said.
Speaking at a press conference on Thursday, Mr Biden hailed his administration’s work in bringing home Americans who had been detained abroad on false or dubious charges.
“Make no mistake – this work is not easy. Negotiations are always difficult and there are never guarantees. I have to make the hard calls and protect American citizens anywhere in the world,” he told reporters.
Earlier, Mr Biden tweeted to confirm Ms Grine was “safe” and “on her way home”.
Cherella Watson, Ms Griner’s wife, spoke of her joy after hearing she had been released.
“Over the last 9 months you have all been so privy to one of the darkest moments of my life,” she told reporters.
“Today I am standing here overwhelmed with emotion but the most important one I have right now is sincere gratitude for Joe Biden and his administration.”
At the time of her arrest, Ms Griner was on her way to Ekaterinburg, east of Moscow, to rejoin her club for the playoffs after spending time in the US.
She was detained at Moscow's Sheremetyevo airport on February 17 with vape cartridges that Russian authorities claimed contained cannabis oil.
The player had a prescription in the US for medical marijuana to relieve the pain from chronic injuries.
She pleaded guilty to the charges of possessing and smuggling illegal drugs but insisted she had made an "honest mistake" and had not intended to break Russian law.
Mr Biden said the US would continue to work to free Paul Whelan, a former Marine, who the president said Russia was treating differently.
"Sadly, for totally illegitimate reasons, Russia is treating Paul's case differently than Brittney's. And while we have not yet succeeded in securing Paul's release, we are not giving up. We will never give up," he said.