The tourists, who included a 10-year-old child, had to spend the night in the tiny cabins high over the glaciers of Mont Blanc after the cable cars became stuck on Thursday afternoon.
The 1950s built cable cars, which connect Aiguille du Midi (3,842m) on the French side of the mountains with Pointe Helbronner (3,462m) on the Italian border, stopped after cables became tangled in high winds.
"It restarted five minutes ago, the last cable (which was blocking the system) was untangled," Mathieu Dechavanne, the head of the operating company said just before 8am (0600 GMT).
That means the remaining passengers were able to be rescued without having the need for helicopters.
Later on Friday morning France's interior minister Bernard Cazeneuve confirmed that the operation to rescue the passengers had ended and all were safe and sound.
On Thursday some 77 tourists were rescued by helicopter but 33 were forced to spend the night hundreds of metres off the ground.
They were due to be airlifted out by helicopter on Friday morning but then just before 8am the cables, which had become crossed on Thursday, became untangled meaning the cable car was operational again, reports in France said.
The 33 tourists had to endure not just the fear of being hundreds of metres off the ground but also temperatures close to freezing.
They were given special survival kits including energy bars and emergency blankets. Specialist rescuers spent the night in some of the cabins, including the one where the 10-year-old child was to try to reassure the tourists.
However one cluster of cabins could not be reached and the occupants had to spend the night alone.
“We were in contact with them throughout the night, the people were cold but there was no vital distress,” said Stephane Bozon from the specialist mountain military police in Chamonix.
On Thursday rescuers faced a battle against time and fading light to bring all the trapped tourists down but conditions meant it was impossible to evacuate them all.
On Thursday weather conditions were at first good but later deteriorated turning cloudy at the high altitudes.
"We succeeded in evacuating, in very difficult conditions, 60 people in an hour and a half," the prefect of the Haute-Savoie region, Georges-Francois Leclerc told AFP.
"We had to suspend the air transport rescue at nightfall," he added.
One of the rescued passengers told local radio: "The last hour was very, very long. We called the company who explained that three cables were tangled and that they were not able to untangle one of them."
The rescue operation involved three helicopters from Switzerland, France and Italy.
An investigation is expected to be launched to find out how the cables became tangled in the winds.
The cable cars offer panoramic views of Mont Blanc, which straddles the French-Italian border.
The incident comes five years after around 40 people were stuck for nearly seven hours on the Grande-Motte cable car in the southeastern French Alps after it broke down.
They were evacuated through trap doors in the floor of the cars, using ropes to reach the ground 40 metres (130 feet) below.