Stausholm replaces J-S Jacques, who was forced to resign over the Juukan Gorge blast.
Stausholm joined Rio in 2018 as CFO and executive director from Maersk.
A University of Copenhagen graduate, Stausholm spent 19 years with Royal Dutch Shell before joining ISS in 2008 and then Maersk in 2012.
Rio chairman Simon Thompson said Stausholm had made a significant contribution to the company since joining.
"His blend of strategic and commercial expertise, strong values and a collaborative leadership style are the ideal qualities for our next chief executive," he said.
"He has a proven track record as a senior executive with deep industrial and resources experience spanning strategy development and technology, as well as financial and risk management. He has also demonstrated the ability to build effective relationships and has a strong personal commitment to the role of business in promoting sustainable development."
Stausholm said he was truly delighted and humbled to be given the opportunity to lead Rio.
"Since I joined two years ago, I have spent extensive time at our operations, meeting our excellent people and have also engaged with many of our valued partners," he said.
"Rio Tinto's purpose is to produce the materials essential to human progress and I remain deeply committed to this after the difficult times we have faced during 2020.
"I look forward to leading Rio Tinto and working with my colleagues across the business to ensure that we maintain strong safety, operational and financial performance, while progressing our growth, sustainability and technology strategies.
"I am also acutely aware of the need to restore trust with traditional owners and our other stakeholders, which I view as a key priority for the company."
Stausholm will be paid a base salary of £1.15 million, plus bonuses and incentives.
Jacques, who announced his resignation in September, will step down as CEO and executive director on January 1 and leave the company on March 31.
"I would like once again to acknowledge J-S's strong leadership of Rio Tinto since 2016," Thompson said.
"He leaves the group in an exceptionally strong financial position, having delivered significant shareholder returns, sector-leading profitability and value creation, and an outstanding safety performance. J-S and the team have created a very solid foundation for future success."
Rio group controller Peter Cunningham has been appointed as interim CFO.
Shares in Rio closed 1.8% higher at A$116.44, close to a decade high.