Cunningham has been interim CFO at the mining giant since 1 January 2021 when his predecessor Jakob Stausholm was moved up to the top job.
"I am delighted to confirm Peter in the role and, having worked closely with him for a number of years, I know he is the ideal person to be our chief financial officer,” said chief executive Stausholm. “His detailed knowledge of the company and of the financial and non-financial drivers of our industry will be invaluable as we continue to strengthen Rio Tinto."
Cunningham will also join the board as an executive director with immediate effect.
He will receive a base salary of £700,000, which could rise to about £4.9mln a year with the addition of a bonus and long-term incentive plan award.
Last month, the FTSE 100 miner faced a shareholder revolt over the salary paid to its former CEO who was forced to step down after the destruction of the 46,000-year-old Juukan Gorge heritage caves in Australia.