His family and lawyer said in a statement that Namazi, 85, flew to neighboring Oman’s capital, Muscat, on Wednesday.
He was scheduled to travel to the United Arab Emirates later for a surgery to clear a “severe blockage” of an artery, they added.
Meanwhile, Baquer Namazi’s son Siamak, who also has been detained since 2015 for similar charges, was given seven days of furlough for the first time in seven years of imprisonment.
Both had been sentenced to 10 years in jail.
In 2018, Baquer Namazi was placed under medical furlough, but continued to face a travel ban.
Iranian media have said Namazi was released as part of an agreement with the US in exchange for the release of billions of dollars of Iranian national assets frozen in South Korea due to the US sanctions on the Islamic Republic.
Observers believe the gestures by Iran and the US are positive signals aimed at facilitating the talks on reviving the 2015 nuclear agreement.