Dubbed the Rose Bowl, the proposals for the site, behind the city's Civic Hall, feature a central, cylindrical auditorium building.
The £130 million scheme, which is about to be submitted for planning, is part of a major reshuffle for the university.
It is understood that LMU has also bought the famous former BBC building on Woodhouse Lane, which will reopen in February 2007 as Old Broadcasting House - a meeting-place for students, as well as those engaged in the arts and enterprise.
There are also plans to build a new 'learning environment' for the Faculty of Arts & Society.
Stephen Willis, director of finance for LMU, said: 'Leeds Metropolitan means business.
'We would like to thank Leeds City Council and others for their support in this venture, which is a valuable development for the city, its people and businesses.'
It is hoped that building work will start this summer, with the building due to open in September 2008.