"I feel very happy. I am exhausted but very happy," said Kopp, who was accompanied by French champion skydiver Mario Gervasi.
The pair were in freefall for 1,000 metres and then used parachutes before landing on a specially prepared platform at 4,500 meters' height.
Preparing for the jump was "very painful" and left his whole body hurting,Kopp said.
Multiple sclerosis is a degenerative disease of the nervous system which disrupts the brain's ability to communicate with the body.
Muscles weaken, lesions emerge on the brain and spinal cord and patients can lose the ability to speak or walk.
Kopp, from Longwy in eastern France, is usually dependent on a wheelchair but trekked through the Himalayas in Nepal for several days on a horse.
He raised 26,000 euros for the trip from friends and well-wishers.
Doctors who examined him after the jump said he had suffered no injuries but advised him to rest for a day.