The analyst was nominated by a group of students at the university who said they had received his approval through his lawyer.
The group said: "We are incredibly delighted to see Edward Snowden elected as the new rector of Glasgow University."
The statement said the institution had a "virtuous tradition of making significant statements through our rectors".
It added: "Our opposition to pervasive and immoral state intrusion has gone down in the records.
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Snowden received temporary asylum in Russia in August -- a move that infuriated the United States -- and is believed to be living in the Moscow area.
Previous holders of the rector's post at Glasgow University include Winnie Mandela and Israeli nuclear whistleblower Mordechai Vanunu.
The current holder is former Liberal Democrat party leader Charles Kennedy.