The 36-year-old, who played 324 Championship matches and was once sold for £2.7million, is hoping to help the Ducks secure a sixth promotion in seven years and reach the National League North, formerly the Conference North.
They are also two wins from the FA Cup first round. Norris said: "I wanted to play for an ambitious club and one where I could potentially win trophies.
"They have done so well in the last few seasons and hopefully I can help them carry it on. It's a bit too early to tell how well we will do this season but I think we've got a chance of promotion. It's a good pitch (at Athersley Rec where Shaw Lane groundshare) and hopefully the club will start building up the fanbase which would be good."
Norris began his career with Boston United and Bolton Wanderers before spending six years at Plymouth Argyle then moving to Ipswich for £2.7million in 2008. He then played for Portsmouth as well as Leeds United, Peterborough, Yeovil and Blackpool before dropping into non-league football last year.
He runs a gym in Bolton, where he lives, and one in Wakefield. He heard about Shaw Lane through a colleague who knows the manager Craig Elliott. He said: "It's different to the football I was playing a few years ago but I still enjoy it and get that buzz when we win. I started off in non-league so it's not a huge culture shock to come back to it. It's still just football."
Norris faced Barnsley FC 16 times for five different clubs and scored against them in their 2-0 loss in Portsmouth in October 2011. He said: "Oakwell was always a really tough place to go and I don't remember getting too many good results there. Obviously playing there for Leeds was a big one. It wasn't a successful ground for me over the years but hopefully I can be more successful down the road with Shaw Lane."
The Ducks won in the second FA Cup qualifying round 2-1 at National League North side Blyth Spartans, with the 90th-minute winner coming from Damien Reeves who netted an FA Cup winner for Altrincham against Barnsley in 2015. They will now play Lancaster – who beat them away in the league earlier this month – at home in the third qualifying round on September 30, with the winner going through to the fourth and final qualifying round.
If they win their next two games in the famous competition, they will reach the first round proper and could draw a club from League One or League Two. Norris played against Chelsea three times in the FA Cup.
"I've been lucky with the games I've played in the FA Cup in the past. It would be nice to have another long run this season. We've definitely got a chance of getting to the first round and it would be fantastic for the club."
Blyth are fourth in the division above Shaw Lane, the National League North which was formerly the Conference North. Paul Clayton put the visitors ahead in the sixth minute but Blyth levelled ten minutes into the second half then Reeves got the winner.
Shaw Lane then won 3-2 at home to Workington in the Evo-Stik Premier on Monday. Clayton put the Ducks ahead but Workington levelled just before half-time. Reeves made it 2-1 then, after the visitors levelled again, Alex Byrne got the winner. The result took Shaw Lane to the top of the table with 21 points from ten games but results later in the week moved them down to second on goal difference behind Witton Albion.