Video footage captured 11 members of the public and two staff members being winched to safety from the Festival Pier attraction - a 53m (174ft) tower, which gives 360-degree views of the coastline - by a Coastguard helicopter.
Dorset and Wiltshire Fire and Rescue Service was called to the scene just after 4.10pm on Tuesday afternoon after engineers' efforts to free the stuck gondola failed.
Firefighters ascended the tower to provide support and reassurance to those trapped, the service said in a statement.
It said most rescue options were discounted on the grounds of safety due to the inclement weather, adding: "At approximately 7.30pm, the Coastguard helicopter started to winch those trapped to safety."
After all passengers were safely returned to the ground, Jurassic Skyline's operator apologised and said the attraction will be closed on Wednesday.
The Jurassic Skyline account tweeted: "We apologise to all those involved.
"A full investigation into the cause of the stoppage is under way."