The Scottish Football Association has confirmed Gordon Strachan's side will meet the Scandinavians on November 19 with the venue still to be confirmed.
Strachan's men host the United States at Hampden four days earlier.
Scotland will be looking to continue the momentum gained from winning three of their last four qualifiers in an otherwise disappointing World Cup campaign.
Strachan, whose side rounded off their group games with a 2-0 win over Croatia on Tuesday, said: "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.
"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."
Scotland's last trip to Norway ended in a 4-0 World Cup qualifying defeat defeat under George Burley in Oslo in August 2009.