The move comes with Stuart unsure where he'll be playing his rugby next season. "My contract with them (Glasgow) has expired and nothing has been fixed up for next season. I hope that my return to the Scotland scene will speed things up.''
Paterson suffered a triple fracture of his right cheekbone in the 38-3 victory over Samoa and has had surgery.
"I'm a bit surprised to get the call," said Stuart. "I've been watching new players coming in for the past week and got to the point where I thought I was about the only international who wasn't involved any longer, so it's nice to finally get a call and feel you are still wanted.
"I was actually preparing to fly out to Portugal to play for the Barbarians in a centenary match on Thursday, which I was looking forward to, but there is no doubt that I'd much rather be flying to Australia to be part of the Scotland squad."
"It has been a while waiting for another chance," said the Stuart, before heading to Edinburgh Airport last night, "but it's great now to get the call. I have no idea whether I'll have a chance of being part of the test squad for the Wallaby matches, but we'll just have to wait and see."
Stuart won three caps for Scotland in 2002, making a try-scoring debut against Romania and playing in the 21-6 win over South Africa a week later.
Scotland play the Wallabies in Melbourne on Sunday and at Sydney's Telstra Stadium a week on Saturday.