The 25-year-old links up again with Town boss Richie Barker, who he also played under at Bury.
Jones told the club's official website: "I'm delighted to be here. Crawley are a progressive club who have got used to success over the past couple of years and this is a great challenge for me at this stage of my career.
"I know Richie well, the way he works and the way he likes his teams to play and I'm looking forward to showing the Crawley fans what I can do."
Barker added: "Mike is a player I know extremely well and I'm delighted to have him on board.
"He's versatile in so much that he can play in central midfield or on the right-hand side so he will bring competition for places in an important area of the pitch. He is a fantastic pro and a very skillful individual and I'm sure he is going to be very popular with our supporters."