Kwarasey appeared in seven matches for the Timbers this before sustaining a finger injury in April.
He recently returned to full health, but found himself second-choice to Jake Gleeson thanks to the New Zealander’s outstanding performances during his absence.
“On behalf of the Timbers, I would like to sincerely thank Adam for his major contributions to the club, both on and off the field, and for his instrumental role in helping the Timbers win their first MLS Cup,” said Timbers general manager and president of soccer Gavin Wilkinson in a club statement.
“This transfer gives the Timbers flexibility to strengthen the team and is a move that makes sense for Adam, his family and the Timbers. We wish him all the best in his career.”
Prior to joining the Timbers, Kwarasey made 154 league appearances over eight seasons with Strømsgodset of the Tippeligaen, Norway’s top flight, winning a league championship with the club in 2013.
Currently atop the Tippeligaen table, Rosenborg have won 23 league titles, nine Norwegian Cups and are the league’s reigning champions. The club has played in the UEFA Europa tournament in five consecutive seasons and are currently in the midst of qualifying for the 2016/17 UEFA Champions League; Rosenborg will carry a 3-1 advantage into Wednesday’s away leg of their two-legged series vs. Swedish side Norrköping.
“I want to thank Adam for his contributions to the club and for helping us win our first major trophy,” said Timbers head coach Caleb Porter. “I enjoyed working with him, and he was a top-class professional in his time here. We wish him nothing but the best with his new opportunity.”