The match against Australia will be played on Saturday 20 November with a 2.45pm kick-off.
Bill Nolan, chairman of Glasgow Warriors, welcomed the news, telling Glasgow's official website: "This announcement is another great piece of news for Glasgow, coming as it does on the back of the very successful IRB Under 21 World Championship earlier this year and the recent announcement about the redevelopment of Scotstoun Stadium. It demonstrates clearly the benefits that can be derived from working closely with public-sector partners, and, in this instance, we are very grateful for the continuing support of Glasgow City Council in enabling us to stage an international Test match at Hampden.
"Such a high-profile event will not only promote rugby within Glasgow but across the entire district, and I am confident that rugby supporters in this part of Scotland will turn out in large numbers, particularly as no club rugby will be played that day. The BT Cup games that weekend have already been scheduled by the Championship Committee for the Sunday."
David Jordan, Glasgow Warriors's chief executive, also expressed pleasure at the news as well as adding his appreciation of the City of Glasgow Council's ongoing backing for rugby. "We continue to enjoy the support of Glasgow City Council, whose investment in world-class amenities such as the strength and conditioning facility at the Palace of Arts has provided Glasgow Warriors with a significant edge for the development of rugby in the district."