The 61-year-old chaired the General Assembly in 2013 and is also an Honorary Chaplain to the Queen.
Last year, she made it onto BBC Radio 4's Women's Hour list of the top 100 most powerful women in the United Kingdom.
The ceremony, which is part of the university's winter graduate programme, is taking place at Bute Hall.
A number of high-profile individuals from policing, justice and medicine are also being honoured.
Vice principle Professor John Briggs say "all are recognised as leaders both within their own fields of expertise and beyond".
Also being honoured by Glasgow University later are:
- Karyn McClusky (co-director of Police Scotland's Violence Reduction Unit)
- Lord Patrick Stewart Hodge (a Justice of the UK's Supreme Court)
- Parveen Kumar (Professor of Medicine and Education at London's St Bartholomew's hospital)