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 carried out a consultation over the name change earlier this year with three alternatives being proposed: Leeds Beckett, Leeds Headingley and Leeds Ridings.
Beckett was chosen in July and a formal application was submitted. The university 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.
“This development is the next exciting milestone in our university’s rich history.”
Sir Bob Murray, 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.”