"I am happy to finally be home. It's been a very long road, a very long journey. Unfortunately, many people have travelled this road with me," he said.
The son of Iranian immigrants, he was arrested while visiting family in Iran in 2011 and accused of being a US spy, a charge his relatives and the United States deny.
He was sentenced to death the following year but that was commuted to a 10-year prison term.
Hekmati said he was "healthy, tall and with my head held high".
"It's great to be back in Flint, my hometown. I love this city. I love its people. They have been so good to me and my family and we are very grateful," Hekmati said.
Abedini, a naturalised US citizen of Iranian origin, arrived at the Billy Graham Training Centre at The Cove, a Christian conference centre in Asheville, North Carolina, that is linked to popular evangelist Billy Graham.
"He arrived safely in Asheville," said Todd Shearer, a spokesman for the Graham family.
Abedini was sentenced in 2013 to eight years in prison after being accused of harming Iran's national security by setting up home-based churches in Iran.
He was reunited with his parents today, his wife said.
- Reuters