"Good news, a plane carrying Dr. Sirous Asgari has taken off from America. Congratulations to his wife and family," Zarif wrote in a post on his Instagram account.
Asgari was accused by a US court in 2016 of stealing trade secrets while on an academic visit to Ohio, but the 59-year-old scientist from Tehran's Sharif University of Technology was acquitted in November.
The academic told British newspaper The Guardian in March that the Immigration and Customs Enforcement agency was keeping him in a detention center in Louisiana without basic sanitation and refusing to let him return to Iran despite his exoneration.
The US agency database still listed Asgari as being detained in the state of Mississippi, AFP reported.
On Monday, Iran's Foreign Ministry Spokesman Seyed Abbas Mousavi said Asgari's case was closed and that he was likely to return to the Islamic Republic within two or three days.