Mr Snowden, who is currently in Russia, is a former US National Security Agency contractor who fled the US after releasing classified documents detailing American and allied spying programmes to the media.
The rector’s main role at Glasgow is to represent the university’s students. Mr Snowden will take over from the previous rector, Charles Kennedy, former leader of the Liberal Democrats.
Other holders of the post include Ross Kemp, the formerEastenders actor.
In a statement to the Guardian, Mr Snowden described the vote as a bold and historic decision in support of academic freedom. “In a world where so many of our developing thoughts and queries and plans must be entrusted to the open internet, mass surveillance is not simply a matter of privacy, but of academic freedom and human liberty,” he said.
Voting took place under a single transferable voting system.
After the first round of voting, Mr Snowden won just over half of the 6,560 votes cast.
He beat three other candidates for the role: the author Alan Bissett; Kelvin Holdsworth, the provost of St Mary’s Cathedral in Glasgow; and Graeme Obree, described on his manifesto page as a “writer, commentator, cyclist and speaker”.
Mr Snowden’s manifesto page states that Glasgow students “have a long and proud tradition of electing student rectors to represent their political views – from Albert Lutuli to Winnie Madikizela-Mandela and, in 2005, the Israeli whistleblower Mordechai Vanunu”.
It continues: “Edward Snowden’s chilling revelations are well known, and their scope far too wide reaching to reiterate here, but what is abundantly clear is that all of our personal communications are now subject to invasive scrutiny by state security. This is not acceptable.”