It's the latest in what has been decades of prisoner swaps between the two countries. The Americans include Siamak Namazi, held since 2015, and Morad Tahbaz and Emad Shargi, both detained in 2018.
The death of a young woman in Iranian morality police custody sparked months of protests and a violent crackdown by the government. A year later, a more subdued defiance endures.
Swedish lawmakers had said they would boycott this year's Nobel Prize ceremonies in Stockholm after the foundation initially invited representatives of the three countries to attend.
A group believed to be linked to Iran fired a drone that killed one U.S. contractor and injured six others, the Pentagon said. The U.S. retaliated, and also faced a second attack on Friday.
Revelers feast and jump over fire to mark the beginning of the new year, but recent protests across Iran and the faltering economy have cast a pall over this year's celebrations.
Saudi Arabia and Iran are restoring full diplomatic relations in a deal brokered by China, a move that could reduce tensions in the region and that asserts China's growing influence in the Gulf.