The company said Mr Thompson will not seek re-election at the miner's 2022 annual general meeting.
Rio Tinto's reputation remains dented after the destruction of 46,000-year-old rock shelters at Juukan Gorge in Western Australia last year.
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Rio Tinto chairman Simon Thompson will step down from his position in 2022.(Rio Tinto)
"I am proud of Rio Tinto's achievements in 2020, including our outstanding response to the COVID-19 pandemic, a second successive fatality-free year, significant progress with our climate change strategy, and strong shareholder returns," Mr Thompson said.
"However, these successes were overshadowed by the destruction of the Juukan Gorge rock shelters at the Brockman 4 operations in Australia and, as chairman, I am ultimately accountable for the failings that led to this tragic event.