The former US National Security Agency contractor fled from his homeland last May after revealing extensive details of internet and phone surveillance.
He is currently staying in Russia where he has temporary asylum.
The rector is the students' elected representative. Mr Snowden succeeds the Liberal Democrat's former leader Charles Kennedy.
Mr Snowden beat three other candidates to the post - cyclist Graeme Obree, author Alan Bissett and Scottish Episcopal clergyman Kelvin Holdsworth.
Previous rectors at the university include Winnie Mandela and Mordechai Vanunu.
http://www.bbc.co.uk/news/uk-scotlan...-west-26243567