The 26-year-old returns to Fir Park after a brief spell with the Steelmen in 2008 when he spent six months at the club as backup under then boss Mark McGhee.
Nielsen - who has been capped 14 times for the Faroe Islands - told MFC TV: "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.
"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 number one and do really well. We finished second last season and if we can do that again it would be a great achievement."
- Sports & Recreation