The change will come into effect at the start of the next academic year in September 2014.
The move sparked controversy earlier this year with almost 4,000 people joining a protest group on the social networking site Facebook calling for the Leeds Met name to be retained.
The university had carried out a consultation over the name change earlier with three alternatives being proposed: Leeds Beckett, Leeds Headingley and Leeds Ridings.
Beckett was chosen in July and a formal application was submitted by the university’s board.
Leeds Met announced yesterday that the move had been approved by the Privy Council, which rules on university name changes.
Professor Susan Price, Leeds Met’s vice chancellor, said: “Beckett Park is where a number of our predecessor colleges were established, the first being the City of Leeds Training College which welcomed its first students in 1913 and is still home to our Headingley Campus, which until 2003 was named Beckett Park Campus.
“Later, Carnegie Physical Training College, the highly renowned centre of excellence for physical education was also established on the campus. This development is the next exciting milestone in our university’s rich history.
“Our commitment to our students is at the core of everything we do; we are an ambitious university and look forward to an exciting future under our new name.”
Sir Bob Murray, the chancellor of the university, added: “We will be very proud to adopt a new name for our university which is so closely linked to the location and birthplace of two of our major founding colleges, fusing our rich educational heritage with our dynamic modern approach.
“We are now looking ahead to the future, building on our recent successes and rapid development.”
Leeds Met had previously planned to change its name to Leeds Carnegie University.