The Scots suffered a heartbreaking exit from England 2015 when a controversial last-gasp penalty call from referee Craig Joubert cost them a 35-34 defeat to the Wallabies at Twickenham.
But they will face their quarter-final opponents a year on, after confirming Michael Cheika’s side will open a three-match series on November 12.
The Murrayfield clash will be followed by Tests against Argentina on November 19 and then Georgia on November 26 - the first time the Lelos have toured Scotland.
Cotter will hope his team can match the feat managed by former head coach Andy Robinson’s 2009 side, who beat the Australians 9-8 in a memorable Edinburgh encounter.
Argentina reached this year’s World Cup semi-finals but the Pumas shipped four tries to the Scots on their last Murrayfield trip last year as they went down 41-31 in the capital.
Scotland have faced Georgia just once before, when stand-off Dan Parks scored all of his side’s points in a 15-6 win during the 2011 World Cup.
Scottish Rugby chief operating officer Dominic McKay said: “We’re delighted to confirm three very exciting matches for November 2016 - World Cup finalists, Australia, World Cup semi-finalists Argentina and an historic first Test on Scottish soil against Georgia.
“We have had many fantastic matches against Australia and Argentina at BT Murrayfield in the past and we’re looking forward to more of the same when they come to Edinburgh next year.
“The Georgians won over thousands of new fans with their performances in the Rugby World Cup, defeating Namibia and Tonga to take them from tournament debutants in 2003 to securing automatic qualification as one of the top 12 teams in RWC 2019.
“I’m sure they’ll get a great reception when they come to Scotland for the first time for this historic Test.”
Kick-off times for each of the three matches have still to be confirmed.