It will be Scotland's first international to be played in Glasgow since Romania were beaten 60-19 in a World Cup warm-up match in 1999.
SRU chief executive Phil Anderton said: "As we have been able to secure an additional Test against Australia we believe it makes sense to showcase international rugby in other parts of the country to allow more Scots the chance to be part of the Scottish rugby experience."
Scotland's most-capped hooker, Glasgow's Gordon Bulloch was born and bred in the city and welcomed today's announcement.
He said: "It's always a magical moment to represent your country but to do so in Glasgow would be extra special for me."
The autumn Test series will start with the first meeting with Australia at Murrayfield on November 6 to mark the opening of the new Scottish Parliament building.
Scotland play Japan at McDiarmid Park the following Saturday and Australia at Hampden on November 20 before returning to Murrayfield for a Test against South Africa on November 27.