Saray Khumalo, 47, reached the top of the 8,848-metre (29,029-foot) mountain after three previous bids were thwarted by bad weather, injury and tragedy.
Khumalo's Summits with a Purpose expedition organiser said she was the first black African woman to reach the top of Everest.
Nepal's Tourism Department confirmed that Khumalo had made the summit but had no record on whether she was the first black African woman.
In 2017, strong winds and frostbite forced Khumalo to give up on Everest, just metres from the summit. In 2015, her expedition was cancelled after an earthquake hit Nepal.
All Everest climbs were halted during her first attempt in 2014 when an avalanche killed 16 guides on the mountain. Khumalo is on a quest to conquer the highest peaks on each continent.
In 2003, South African park ranger Sibusiso Vilane became the first black person to summit Mount Everest. Khumalo uses her expeditions to raise funds for libraries and support children's educational activities.
"My dream is to go higher and go further for as long as I breathe. To pave a way for my children and other ordinary people, so we may realise and accept that ordinary people like us can achieve extraordinary heights," Khumalo says on her website.
The death toll is already mounting, however.
Two Indian climbers have died and a Chilean is missing on Mount Kanchenjunga, the world's third-highest mountain, expedition organisers said.
Biplab Baidya, 48, and Kuntal Karar, 46, were on the 8,586-metre (28,169-foot) mountain on the Nepal-India border with a five-member team from India's West Bengal state. An operation was started to retrieve their bodies.
Last week, Peruvian climber Richard Hidalgo died on Mount Makalu, the world's fifth-highest mountain, while a Malaysian died in April after being rescued from Mount Annapurna, where he spent two nights in the open near the summit.
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