Elite Expeditions shared the news in a post on social media, saying it was with "profound sadness and immense heartbreak" that it confirmed Purja's death in Thursday's avalanche.
It also said it had received confirmation that the other nine members of the expedition had not survived.
The Nepal-born climber was known for scaling the world's 14 highest peaks in just over six months in 2019.
Pakistani officials previously said the bodies of three climbers - American Mallory Geis, Nadhira Ahmed Abdullah Al Harthy from Oman and Pur Bahadur Gurung from Nepal - who were among the 10-person expedition had been recovered.
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