Mr Snowden was inducted into the role in a ceremony at Bute Hall in which he spoke to an audience of 250 students via a live wireless link with Russia, where he has been given temporary asylum.
Despite overwhelming support for his campaign from students, several key campus bodies have raised concerns about the ability of an absentee rector to represent students - a key role of the post.
A page on the social networking site Facebook run by students dedicated to his campaign reflected this view, with one comment stating: "Hope he's taken some time to understand the university and its students."
However, Jess McGrellis, the president of the university's Student Representative Council (SRC), said discussions between Mr Snowden's representatives in the US and university officials had been positive.
She said: "It was really nice to hear in his speech of his willingness to engage with the student body and to be interested in the university.
"We will do everything we can to facilitate his involvement. He seems very happy to have surgeries with students and there may also be issues that students are interested to talk to him about.
"There has been an indication that he is wanting to have communication with students using video links, and that would be very interesting."
Chris Cassells, a student who nominated Mr Snowden, also stressed the rector's willingness to engage with his role. "Everyone hopes that he will stand up for the students of Glasgow. Where there is a will there is a way," he said.
Mr Snowden, who fled America, via Hong Kong, in May last year having leaked evidence of extensive internet and phone surveillance by US intelligence, was named as the university's rector in February.
He defeated the former champion cyclist Graeme Obree, the author Alan Bissett and the Rev Kelvin Holdsworth, who also stood for the post.
He takes over from Liberal Democrat MP Charles Kennedy and will hold the office for the next three years.
The role of rector is to represent student issues to senior management at the university, but previous incumbents have been elected as political statements.
Winnie Mandela was elected in 1987 and Israeli whistleblower Mordechai Vanunu became rector in 2005, despite students knowing that neither would be able to travel to Glasgow and take up the practical role of the position.
However, in recent times the rectors have held face-to-face surgeries for which any registered student can make an appointment.
The surgeries provide an opportunity for students to speak to the rector about any issues they feel are of concern.