"Brynjar is an all-action midfield player in the mould of Phil Parkinson who has excellent fighting qualities and is full of energy, but also has the ability to score goals," Roylas director of football Nick Hammond has said.
"He should not be viewed as a straight replacement for Andy Hughes because we have been working all summer to bring him to the club."
Gunnarsson will now fly out to join up with his new team-mates who are on a pre-season tour of Sweden.