The 26-year-old, who spent six months on loan at the SPL club in 2008, arrives from Danish club Silkeborg on a two-year deal.
Nielsen counts Blackburn and Manchester City among his former clubs and will challenge Lee Hollis for a first-team place at Fir Park.
He told the Motherwell website: "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 No 1 and do really well.
"We finished second last season and if we can do that again it would be a great achievement."