At the rector installation ceremony at the university, Snowden presented his inaugural address via video link to staff and students, Xinhua reported Wednesday.
"In a democracy people have a right to know the policies of their government. This idea that if we believe in something we should stand up for it is what I will follow in my role as rector of the university," Xinhua quoted Snowden as saying.
Jess McGrellis, president of the University of Glasgow's students' representative council, said he was "happy that Snowden was able to continue the tradition of addressing students at this installation."
The main role of the rector is to represent the university's students, the report said.
Having received 3,347 of the 6,560 votes cast by students in February, Snowden takes over from his predecessor Charles Kennedy and will hold the office for the next three years.
Snowden, a former US defence contractor who revealed the country's secret surveillance programs, is currently living in Russia under temporary asylum and facing espionage charges for his leaks on US National Security Agency surveillance practices in his home country.