Among those she thanked were President Barack Obama, Hillary Rodham Clinton, the secretary of state, North Dakota politicians, human-rights groups and the Japanese government.
She said that singing the national anthem helped keep her going.
"It may sound corny, but I'm so happy to be home in the land of the free," said Saberi, 32, who has dual Iranian and US citizenship.
Saberi was freed on May 11 and reunited with her parents, who had come to Iran to seek her release, after an appeals court reduced her sentence to two years suspended.
She spent a week in the Austrian city of Vienna recuperating.
Saberi plans to spend a few days in Washington before returning to her home state North Dakota, according to Earl Pomeroy, the state's Democratic House member.
He issued a statement saying he was eager to welcome her home.
Saberi grew up in Fargo, North Dakota, and moved to Iran six years ago.
Kevin Melicher, a neighbour of Saberi's parents in Fargo, said the community prayed for Saberi's return and planted flowers in her family yard earlier this week.
"They wanted to do something," he said. "We want to make their house look welcoming."