Simon Thompson will step down after next year's annual general meetings, while non-executive director Michael L'Estrange, who led the review into the company's handling of the incident, will retire in May.
"I am ultimately accountable for the failings that led to this tragic event," Thompson said in a statement.
Last year's destruction of the 46,000-year-old Juukan Gorge rock shelters in Western Australia for an iron ore mine sparked a massive public and investor uproar.
It remains to be seen, however, whether the latest departures will allow the company to draw a line in the sand over the saga, with some investors suggesting that more heads may have to roll.
"Other Rio Tinto directors who enabled the unhappy regime of the past few years, or who have made excuses for it, are encouraged to reflect on whether their continuing presence on the board is truly in the interest of the company and its shareholders," said James Fitzgerald, a lawyer with activist investor the Australasian Centre for Corporate Responsibility.
In addition to Thompson and L'Estrange, former CEO Jean-Sébastien Jacques is due to leave the company at the end of this month. He has been replaced by Jakob Stausholm who was chief financial officer.
Two senior executives, who were in charge of the iron ore division and corporate relations, the unit responsible for dealing with Indigenous communities, also left last year.
Rio invited further outrage last month when it revealed that Jacques and the two senior executives had all finished 2020 with substantial payouts. Jacques received total remuneration of 13.3 million pounds ($18.6 million) under Australian accounting rules, up from 7.1 million pounds a year earlier.
Thompson and L'Estrange had faced pressure to leave after what was seen as the board's mishandling of an investigation into the destruction that found no single person accountable.
Thompson came under more pressure last month after elders of the Puutu Kunti Kurrama and Pinikura people accused him of breaking a personal promise that Ian Vella, who had been leading reconciliation efforts, would not change jobs until ties had been repaired.
Independent directors Sam Laidlaw and Simon McKeon will lead the search for the new chairperson, Rio said.
National Native Title Council Chief Executive Jamie Lowe welcomed the latest departures at Rio and said there was a dire need for a senior leadership position within the company to be held by an Indigenous person.
He also said it was paramount that there also be significant law reform in Western Australia, which had approved the blasts.
"Without this, it doesn't matter how many leadership changes we see within the mining sector. To adequately manage and protect our cultural heritage, the buck stops with government," he said.
(Reporting by Melanie Burton in Melbourne; Additional reporting by Shashwat Awasthi in Bengaluru; Editing by Richard Pullin and Edwina Gibbs)
By Melanie Burton