Thompson, 23, a product of the Rochdale youth system, scored 17 goals in 157 appearances during six years at Spotland.
The 2007 League Two Apprentice of the Year has opted to stay in League One following Dale's relegation.
Rovers boss Ronnie Moore told the club's official website: "Joe is a great addition to the squad.
"He's got plenty of pace, he's good on the ball and he likes to take the opposition on.
"He can create and score goals and he's strong in the air too. I'm looking forward to working with him."
