Deliveries of the A330s are to begin in 2015 and the A350s in 2018, under the terms of the memorandum of understanding.
SAS said it had also signed an option for six more A350-900s and an upgrade of passenger cabins on up to seven A330/A340s.
The upgrade, to be completed by 2015, would consist of new seats throughout the cabin including fully flat seats in business class, and throughout the entire cabin a new high definition full video on demand in-flight entertainment system.
The order "marks the launch of SAS's long haul renewal plan," the company said in a statement.
"The great technological improvements of this extensive fleet renewal plan give SAS a long haul fleet that will be top of (the) class in the industry," SAS chief executive Rickard Gustafsson said.
"It will truly increase our competitiveness and strengthen our customer offering – both with regard to comfort, service and efficiency. Furthermore, we are able to significantly bring down fuel consumption which will lower our costs and support our goals to reduce emissions," he said.
SAS, which has reported losses for five years running, is in an intense restructuring process after several savings packages failed to yield results.
According to SAS, the company's fleet currently consists of 19 Airbus and 74 Boeings.