Alan Davies, who joined the Rolls-Royce board in 2015, was a non-executive director and member of the British manufacturing group's nominations and governance committee, the audit committee and the safety and ethic committee.
"I am hugely grateful to Alan for the contribution he has made to the board. His expertise and perspectives will be greatly missed," said Rolls-Royce chairman, Ian Davis.
No reason was given for Davies' departure.
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On Wednesday, Rio Tinto announced it had terminated the contracts of Davies, who was formerly the chief executive of its energy and minerals division, and legal and regulatory affairs group executive Debra Valentine.
The company said the executives had "failed to maintain the standards expected of them" under Rio Tinto's global code of conduct, after it opened an investigation into a $10.5m (£8.4m) payment to a consultant advising on the group's huge Simandou iron ore project in Guinea.
Rio Tinto said it became "aware of email correspondence from 2011" relating to the matter. Davies "had accountability" for the project in 2011.
Today, a Guinean former mining minister, Mahmoud Thiam, said the head of Rio Tinto's Guinea operation, Steven Din, offered him a bribe in 2010 to win back control of half the undeveloped Simandou project, Bloomberg reported.
Rio Tinto declined to comment on the claim.
The FTSE 100 group's share price was down three per cent today to 2,930p.