The 38-year-old left-winger will once again be a New Jersey Devil should he pass a physical after Phoenix traded Sullivan for a 2014 seventh-round draft pick before Wednesday’s deadline.
Eligible to become an unrestricted free agent July 5, he has five goals and 12 points in 33 games this season.
New Jersey drafted the five-foot-eight, 160-pound Sullivan in the ninth round (233rd overall) in 1994.
He spent parts of two seasons with the Devils before being traded to Toronto in a deal for Doug Gilmour in February 1997.
Sullivan’s other NHL stops include Pittsburgh, Nashville and Chicago.
He has amassed 288 goals and 454 assists for 742 points in 1,002 NHL regular-season games.