Velayati was handed over to the Embassy of Iran in Kabul on Friday night.
Taliban deputy spokesman Bilal Karimi has confirmed that Velayati has been released.
The Iranian photojournalist had been arrested at the airport of Kabul on August 19 when he was going to board the plane to fly home.
He had legally entered Afghanistan's capital via an aerial border crossing and spent ten days there.
The Taliban had detained him without any explanation.