The computer analyst became a wanted man when his leaks brought to light secret National Security Agency documents which revealed widespread US surveillance on phone and internet communications.
It led to not only embarrassment but also friction with other countries when the extent of the surveillance emerged.
Mr Snowden's passport was revoked and a warrant was issued for his arrest - for passing on classified information and theft of government property - when his leaks came to light.
He is now in Russia, which granted his temporary asylum after he fled the US.
A group of students at the University of Glasgow said he agreed to stand and his candidacy is an "opportunity to show our gratitude to a brave whistleblower, and thus all to other whistleblowers who take risks to reveal the criminality and corruption of powerful groups in the intelligence services and other arms of government, media, police, parliament and military".
His candidacy was announced today as nominations for the position closed.
PhD student Chris Cassells said: "We got in touch through his lawyers and have been communicating through them, and he has agreed to take part and was happy to support what we're doing.
"Our position is that voting for Edward Snowden first of all shows support for his plight at the moment and it also sends a message to governments that the intrusive practices of state security are not acceptable and are not something the students of the university agree with."
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 and fulfil the practical role of the job.
Mr Cassells said: "The university has a long history of electing political rectors like Winnie Mandela or Israeli whistleblower Mordechai Vanunu, so this campaign is along similar lines to that.
"It's only gone public today but so far we've had nothing but support from other students."
Voting for rector takes place over two days next month. Former champion cyclist Graeme Obree, writer Alan Bissett and Kelvin Holdsworth, Provost of St Mary's Cathedral in Glasgow, are also standing in the vote.
Former Liberal Democrat leader Charles Kennedy currently holds the position.
A spokeswoman for the university said: "The University of Glasgow has received the following nominations for the next election of the rector: Alan Bissett, Kelvin Holdsworth, Graeme Obree and Edward Snowden."
She added that all nominees have "personally agreed" to take part in the process, with the vote being held on February 17 and 18.