Stewart, currently Scotland's first diplomat in the US and a former media chief at Glasgow City Council, will take on the new role of head of corporate communications in September.
The post has been created following a brand review last year, which recommended bolstering the university's PR to raise its profile nationally and abroad.
Stewart has been in her current post - at the British Embassy in Washington - for four years, helping to promote Scotland via initiatives such as Tartan Week.
Prior to this she was deputy head of the Scottish Executive press office.
While at Glasgow City Council, she was chief media and information officer.
Stewart will lead a 12-strong team, reporting to university principal Sir Muir Russell. When Stewart arrives, acting director of publicity services Annie Vaz - the university's most senior PRO - will become internal comms head.
'Although the Scottish Higher Education Council has been more generous in its settlement this year, historical universities are facing a legacy of underfunding and need investment for building repairs and money for research faculties,' said a spokeswoman. 'Stewart will be tackling these issues at parliamentary level.'