Scotland will travel to face Norway in a friendly on 19 November.
Gordon Strachan's side concluded their World Cup qualifying campaign with
a 2-0 victory over Croatia
and had already lined up a friendly against the United States next month.
That meeting with Jurgen Klinsmann's team
will take place four days before the Norway match.
Norway, who last met Scotland in 2009, also missed out on a place at next year's World Cup finals in Brazil.
“Facing Norway gives us an opportunity to finish 2013 in better spirits than we started the year”
That last encounter, in Oslo, produced a 4-0 win for the hosts in a World Cup qualifier but the Scots did win on their previous visit to the Norwegian capital.
The venue for the November meeting is yet to be confirmed.
"We enjoyed a fantastic result at Hampden this week against a top-class nation and it is important we continue to challenge ourselves to improve," Strachan
told the Scottish FA website.
"We want to build on the improvement we have seen and facing the United States and now Norway gives us an opportunity to finish 2013 in better spirits than we started the year.
"We want to give the fans reason to be optimistic ahead of the European Championship qualification campaign next year and these next two games give us an opportunity to do so against two highly respected football nations."
Norway coach Per-Mathias Hogmo added: "We are looking forward to playing against Scotland as part of our preparations before the qualifiers for the European Championship in France.
"It's important to play as many games as possible before the qualifying, and Scotland will be a good test for us.
"Its also nice to invite them to Norway. Scotland has fantastic supporters, and I'm sure they will make a great atmosphere at the stadium."