The 33-year-old will count $3 million against the salary cap for the next two seasons after the final three years of his contract was bought out by the New York Rangers in June.
Only goalie Henrik Lundqvist had been with the Rangers longer than Girardi. The alternate captain had spent his entire 11-year career in New York.
Girardi, a 2012 All-Star, has been slowed by injuries in recent years, and his performance has suffered. He had four goals and 11 assists last season, the third straight year his numbers have declined.
The Associated Press contributed to this report.