Nelson, 29, is City's third signing after midfielders Matt Gill and Owain Tudor-Jones joined the Canaries.
He told City's official website: "The club doesn't need much selling to be honest. You come and have a look at the stadium and the training facilities, it's got to be up there with some of the best in the Championship, never mind League One.
"The club as a whole, it's a massive club and everyone I speak to says it's a nice area to live as well and obviously knowing Ian Butterworth down here was a big help as well.
"Having someone I know on the coaching staff to come down to work with will help me along as well."
Nelson will be back at Victoria Park at the end of August, and added: "I was there six years and had some quite successful seasons, but I enjoyed my time up there and made some good friends with the players."