Gordon Strachan's men will be in action on Tuesday, November 19 - no venue has been announced - four days after they host the United States in the final Hampden Park fixture before the national stadium is redeveloped ahead of the Commonwealth Games.
And Strachan is keen to ensure his squad keep up the momentum they have built over the last four games, which saw three victories to end their World Cup qualifying campaign in positive fashion.
"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," said Strachan.
"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 failed to make it to Brazil, like Scotland finishing fourth in their group which was won in impressive fashion by unbeaten Switzerland.
Their coach Per-Mathias Hogmo said: "We are looking forward to playing against Scotland as part of our preparations before the qualifiers for the European Championships 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."