Nelson, 30, has signed a two-and-a-half year contract and moves from Carrow Road foran undisclosed fee.
"It was a bit of a rush but it's done now so I'm over the moon. I'm delighted to sign. Now it's done, I'm just looking forward to getting involved as soon as possible," said Nelson.
"I've had talks with Scunthorpe in the past but, due to whatever circumstances, the move didn't come about. It has done now though. I'm really happy to be here, and I'm looking forward to knuckling down and getting started."
He has been at the Canaries since the start of last season, when he joined on a free transfer from Hartlepool United.
He made 45 appearances for Norwich, but will always be associated with Pools having made 309 appearances for them in a six-year spell in the north-east.