The Swedes were given permission to leave the country on Monday, Foreign ministry spokesperson Joakim Larsson confirmed adding that the ministry has no information about why they were arrested.
Mikael Ekman at film company Pampas production confirmed that the team are expected back in Sweden by Tuesday morning.
“The security police followed them all the way to the plane,” he said.
The three Swedes were arrested shortly before a demonstration was scheduled to take place in the capital city Baku.
The foreign ministry initially though that the arrests could have been due to to visa irregularities.
Mikael Ekman has only been able to confirm that the police erased their memory cards.
“There have been a few different explanations, everything from their visas not being correctly formulated to filming permits,” Ekman told TT.
He said the Swedes had been treated well and haven’t been subjected to any threats or physical violence.