Andrews reached the summit just before dawn on Thursday, according to a post on the American climber's Instagram account. During the hike, guides assisted with oxygen, water and food.
The previous record had stood since 2003, when Nepalese Lhakpa Gelu Sherpa climbed the mountain in 10 hours and 56 minutes.
The new record, which applies to ascents with supplemental oxygen, must be confirmed by Nepalese authorities before it is written into the history books.
Cancer survivor Andrews also tried to break the record without oxygen earlier in May - 22 hours and 29 minutes - but was forced to turn back.
So far this year, more than 950 climbers have reached the summit of Mount Everest. Five people have died on the mountain.
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