Terms were not disclosed.
Brassard has been traded four times since July 2016 and three times in a little over a year. He is coming off a five-year, $25 million contract that he signed with the Rangers.
He had 14 goals and nine assists last season, his worst output in a decade.
The 31-year-old's best season came in 2014-15 with the New York Rangers, when he had 60 points.
Brassard has scored 451 points (176 goals, 275 assists) in 786 games in 12 seasons.