US Army Sergeant Bowe Bergdahl, 28, is being transferred to a German hospital.
He is being exchanged for five Afghan men who were detainees in Guantanamo Bay who were released from the Cuban prison and handed to Qatar who brokered the deal.
In a tearful press release with Bergdahl's parents, President Obama said Qatart would "put in place measures to protect our national security".
He added: "While Sgt Bergdahl was gone he was never forgotten"
Bergdahl was the only prisoner held by the Taliban.
He was handed over on Saturday night in an operation that involved US special forces and is reported to have difficulty speaking English after so long in captivity.
The owner of a wine bar in Hailey and an old friend of Bergdahl, said: "It's very exciting. We're all still kind of walking around on clouds.
"We're all just waiting to get eyes on him. That's going to be a topper."
Bergdahl's parents appeared with Obama at the press conference to announce the release.
His father, who had grown a beard for the length of his son's captivity in solidarity extended thanks "around the world".
He added: "The complicated nature of this recovery will really never be comprehended.
"We just can't communicate the words this morning when we heard from the President.
"So we look forward to continue the recovery of our son, which is going to be a considerable task for our family and we hope that the media will understand that that will keep us very preoccupied in the coming days and weeks as he gets back home to the United States."