The 23-year-old was called up to the Iceland squad in May and is currently out in Russia as stand in to Hannes Halldorsson.
He has three caps and was in goal for Iceland when Mexico beat them 3-0 in March out in California.
"He's technically gifted, has no fear of aerial play and is very good with his feet," said Dijon director Sebastien Larcier.
"He has the right temperament and bags of charisma," Larcier said of the 6ft 2in stopper.
Runarsson, whose father won over 100 caps in the Iceland midfield, has signed a four year deal with the Ligue 1 club after two solid seasons at FC Nordsaelland in Denmark.