Mr Snowden – who has sought asylum in Russia after leaking top secret details of web surveillance by US spy agencies – agreed to stand when a group of students put his name forward for the role.
Former Rectors include Winnie Mandela and the Israeli whistleblower Mordechai Vanunu who revealed information about his country’s nuclear weapons programme to Britain in the mid-1980s.
University officials said there had been a record turnout for the vote, in which the ex-NSA contractor beat former champion cyclist Graeme Obree, the author Alan Bissett and the Episcopal clergyman Rev Kelvin Holdsworth.
Chris Cassells, Mr Snowden’s spokesman for the campaign, emphasised Glasgow University’s “proud and virtuous tradition” of making significant statements through its rectors.
“Today we have once more championed this idea by proving to the world that we are not apathetic about important issues such as democratic rights,” Mr Cassells said.