More than 6500 students turned out to vote - the highest recorded number in modern times and double last year's turnout.
The students who campaigned on behalf of the former National Security Agency intelligence officer gave an acceptance speech on his behalf.
Snowden is currently in Russia after fleeing America, having leaked internet and phone surveillance by US intelligence to the media.
He agreed to run for the Rectorship after being approached by students via his lawyers.
Snowden will now replace Charles Kennedy, the outgoing Rector, to serve a three-year term in the post.
The result of the online election was announced to candidates and their supporters in the Bute Hall shortly after polls closed at 5pm on Tuesday.