It has purchased the majority of a 14 acre site currently occupied by the Western Infirmary.
The site, which is bounded by Dumbarton Road, Church Street and University Avenue in the west end, is next to the university's Gilmorehill campus.
Officials said talks were ongoing with NHS Greater Glasgow and Clyde to secure the remaining part of the site with the hope it will pass to the university in 2015 when the Western Infirmary closes.
The university intends to begin setting out a new campus strategy involving consultation with staff, students, residents, businesses and other interest groups.
There will also be discussions with Glasgow City Council, NHS Greater Glasgow and Clyde, the Scottish Government, Scottish Enterprise and other key bodies on the most appropriate way to develop the site.
However, it is likely new buildings on the Western Infirmary site will enable the relocation of academic activities from buildings no longer considered to be suitable. The university currently occupies several historic sandstone properties.
It is anticipated that any vacated buildings can then be sold, creating income to fund the development of the new site.
The university is already committed to investing at least £80 million in new buildings and equipment and £55m in refurbishing facilities over the next five years.
Professor Anton Muscatelli, principal of Glasgow University, said: "This is as significant a development in the ongoing story of Glasgow University as the relocation to Gilmorehill from the city centre was in 1870.
"The acquisition of the site will allow us a unique opportunity to provide modern, fit for purpose facilities that are in keeping with Glasgow's status as a world leading research-intensive university.
"The student experience is at the heart of all we do, and the campus redevelopment will allow us to focus on what our students want and need, as well as providing an environment that is open and accessible to the wider community.
"We now have an opportunity to create a lasting legacy for future generations of students, academics, local people and for the city of Glasgow as a whole."
Robert Calderwood, chief executive of NHS Greater Glasgow and Clyde, added: "In 1878 the university transferred the land to the former hospital authority to construct the original Western Infirmary.
"The terms of the deal stipulated that, should the site no longer be required for healthcare purposes, the university should be given the opportunity to re-acquire it.
"The Western Infirmary is to close in 2015 and we are delighted a significant part of the site has been sold back to the university for educational purposes."
Gordon Matheson, leader of Glasgow City Council, said: "The acquisition of this site by the university would present an opportunity to develop state of the art facilities that would consolidate and develop the city's status as a leader in education, renewables, research and technology.
"Many people and organisations have a stake in what may be developed, and we look forward to learning more about the proposals."
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