Atkinson, 32, played in the Football League for Barnsley, Rochdale, Grimsby and Accrington, and made 23 appearances in National League North last season.
He said: “I’m really pleased to be here. Paul has really sold what his vision is for the season. Meeting the lads was really good, everyone is in great spirits and is ready to get going.”
Atkinson played for England C in 2011, and also helped Fleetwood Town to promotion to the Football League.
Gingerbreads manager Paul Rawden said: “Getting Rob in has added experienced player with know-how to the squad.
“With Rob being part of the upper end of the non-league pyramid over the last few seasons, as well as his background in the Football League, he will be brilliant for the younger players in the squad.”