Coyotes general manager Don Maloney announced the deal Wednesday.
A source told ESPN.com's Pierre LeBrun that the deal is worth $1.45 million, with Bissonnette paid $725,000 per season.
Phoenix claimed the 26-year-old Bissonnette off waivers from Pittsburgh on Sept. 30, 2009.
The 6-foot-2, 216-pound forward had one goal and a team-high 71 penalty minutes in 48 regular-season games last season.
He has four goals, three assists and 210 penalty minutes in 104 NHL regular-season games with the Coyotes and Penguins. Bissonnette was drafted in the fourth round by Pittsburgh in 2003.
Information from The Associated Press was used in this report.