The fugitive former National Security Agency systems analyst, who leaked his country's intelligence secrets, defeated three other candidates for the University of Glasgow position after 6500 people went to the polls over two days.
The vote is expected to be entirely emblematic as Mr Snowden is in hiding from the US authorities in Russia and it is thought to be implausible that he can take on the role of a working rector.
The role of rector is to represent student issues to senior management at the university but previous rectors have been elected despite being unable to travel to Glasgow to fulfil the practical role of the job.
Mr Snowden said it was an honour to win the student's backing.
He said: "I am humbled by and grateful to the students of Glasgow University for this historic statement in defence of our shared values.
"We are reminded by this bold decision that the foundation of all learning is daring: the courage to investigate, to experiment, to inquire."
He added: "If we do not contest the violation of the fundamental right of free people to be left unmolested in their thoughts, associations, and communications - to be free from suspicion without cause- we will have lost the foundation of our thinking society.
"The defence of this fundamental freedom is the challenge of our generation, a work that requires constructing new controls and protections to limit the extraordinary powers of states over the domain of human communication.
"This election shows that the students of Glasgow University intend to lead the way, and it is my great honour to serve as their rector."
His election came after supporters complained posters of Mr Snowden 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 by the result.
The computer analyst became a wanted man when his leaks brought to light secret NSA documents which revealed widespread US surveillance on phone and internet communications.