He is recovering from hypothermia and exhaustion in a hospital, police said on Wednesday.
The man, a 19-year-old student in Lausanne, Switzerland, disappeared on Sunday while skiing at the Les Diablerets resort.
Without a phone or detection device, he was only reported missing on Tuesday.
Rescue workers using a helicopter found him in a region with a high risk of avalanches.
Police said the man was off-piste or out-of-area skiing without the proper equipment.
He told rescuers that his binding, which attaches the boot to the ski, had broken, causing him to fall into a stream.
Exhausted and wet, he got caught in a snow storm while trying to return to the resort. Police said his clothing helped him survive the freezing temperatures.
"His life is not in danger," police said.
The American's rescue came after 11 off-piste skiers were killed in avalanches in the Swiss Alps over a period of four days, following heavy snow-fall.