ESPN.com's Pierre LeBrun reports the deal is worth $1.85 million plus bonuses.
Sullivan played in Pittsburgh this past season and had 17 goals and 31 assists. The 37-year-old has played 15 seasons in the league with five teams and has 283 goals and 447 assists.
"We are very pleased to welcome Steve to the Coyotes," general manager Don Maloney said. "Steve is an intelligent player who adds skill to our lineup and will help improve our power play. He is a great addition to our roster."