Edds began his career in England as a trainee with Nottingham Forest and joined Dons in 2004 following spells at Bradford and Swindon
Rovers boss Ronnie Moore said: "I'm delighted to have signed Gareth. He's as comfortable at right-back as he is in midfield, so his versatility will be very useful.
"Last season we missed having a box-to-box midfielder and Gareth will provide that.
"He is a hard working, quality player who is a good signing for the club and I look forward to working with him."