The 22-year-old Iceland international, who moved to Wolves from Lillestrom in the summer of 2012, will stay with the Norwegian club until the end of 2014.
"Bjorn has expressed a desire to go and play abroad again," head coach Kenny Jackett told the League One club's official website.
"He feels that the football will suit him better than in England and in particular League One.
"He is going to a very good club in Molde for a year as he tries to re-establish and build his career again."
Sigurdarson's last appearance for Wolves came against Rotherham United in a 3-3 draw on December 21.