The 26-year old Faroe Islands international has penned a two-year deal with the Steelmen, returning to Fir Park following his loan spell in 2008.
"I'm delighted to be back and having been at some big clubs where it was hard to get a game, I can't wait to get playing again," he told the club's official website.
"I know Motherwell well from my six months here before and I know it's a great club to be at.
"I'm really pleased to get this sorted and am looking to establish myself as No 1 and do really well.
"We finished second last season and if we can do that again it would be a great achievement."