CNN quotes a U.S. official as confirming the release.
The news follows reports that a lawyer for the pair had finally negotiated their release.
“I have got necessary signatures from judiciary officials for their release on bail … Hopefully the two will be freed today,” the lawyer, Masoud Shafie, told Reuters.
The Americans, both 29, were convicted of illegal entry into Iran and espionage after being arrested while hiking in July 2009 along the Iran-Iraq border.
The news comes a week after Iranian president Mahmoud Ahmadinejad said Bauer and Fattal, who have proclaimed their innocence, would be freed “in a couple of days” as a humanitarian gesture.
Shafie said there has been an issue with the bail money since then. “There were some problems regarding depositing the bail … We are trying to resolve it with the bank … It will be resolved,” he said.
Shafie said last week the men would be freed on $500,000 bail each. A third American, Sarah Shourd, who was arrested with Bauer and Fattal – and who got engaged to Bauer while in captivity – was allowed to go home on $500,000 bail last September.