The 33-year-old, who attended school in the city, was elected unopposed and assumes the role with immediate effect.
Mr Beaumont succeeds Dundee-born actor Brian Cox, who was elected in 2010 and served two terms.
Mr Beaumont previously held the record for cycling around the world, completing the route in 194 days and 17 hours.
He said: "I am absolutely thrilled, and slightly surprised, to be the new rector of the University of Dundee.
"Six years ago I sat in the audience at the Caird Hall as Brian Cox stepped into the role and I remember his words about making a real difference.
"In fact Dundee was the starting point for my first ever adventure at the age of 12, to cycle across Scotland.
"I look forward to playing my part in the University of Dundee's many future triumphs."
Mr Beaumont will be formally installed as rector in a ceremony to be arranged for a later date.
The rector is elected to serve the students' interests, including at the University Court, the governing body of the institution.
The university's principal and vice-chancellor, Professor Sir Pete Downes, said: "I am delighted to welcome Mark Beaumont into the university community, and I am sure he will be an excellent representative for our students."
Round-the-world cyclist Mark Beaumont has been named the new rector of Dundee University.