The fugitive former National Security Agency systems analyst, who leaked his country's intelligence secrets, defeated three other candidates last night after 6500 people went to the polls over two days.
It came after supporters complained posters of Snowden, who is in hiding from the US authorities in Russia, had been torn down and cut up and some university unions called for an active rector.
After Mr Snowden defeated former champion cyclist Graeme Obree, author Alan Bissett and the Reverend Kelvin Holdsworth, some students said they had been angered at the decision.
Hannah McNeill, who was among those gathered to hear the result at the university's Bute Hall, said: "I'm furious. I think most people here are very upset about the result. We need an active rector. We could have given him (Snowden) an honorary degree or something.
"The only good thing is the number of votes that were cast because it was a lot more than usual."
Meanwhile, Louise Wilson said: "It's very disappointing but not surprising in the slightest.
"I'm all for political statements, but at a time when the university and students need the biggest say with all the cuts it's just inappropriate not to have a working rector."
The computer analyst was nominated by a group who said they had received his approval through his lawyer.
The turnout on Monday and yesterday was double the number during Liberal Democrat MP and Glasgow graduate Charles Kennedy's election as rector for a second time three years ago.
Obree, who dropped out four months into a design engineering degree, said he was not surprised to see Mr Snowden win.
He said: "I can see it both ways. It's important that if he wasn't elected that it wouldn't be used against him, but the students obviously feel quite strongly about what he stood for.
"It was an emphatic win. There were students who wanted a working rector but the votes were split between three candidates. Let's say it was only Kelvin, who got the second most votes, and Snowden, then it might have been a different outcome and certainly would have been closer."
Mr Snowden became a wanted man when his leaks brought to light secret National Security Agency documents which revealed widespread US surveillance of phone and internet communications. He is staying in Russia, where he was given temporary asylum.
The students of Glasgow University have a history of electing rectors unable to take up the practical role of the position. Previous rectors include Winnie Mandela, elected in 1987, and Israeli nuclear whistleblower Mordechai Vanunu, in 2005
A statement by Mr Snowden's supporters said: "We are delighted to see Edward Snowden elected as the new rector.
"We have a proud and virtuous tradition of making significant statements through our rectors and we have once more championed this idea by proving to the world that we are not apathetic to important issues such as democratic rights."