The 30-year-old Grabovski scored 13 goals and added 22 assists for 35 points in 58 games last season with the Washington Capitals.
In 425 career NHL games with the Montreal Canadiens, Toronto Maple Leafs and Capitals, Grabovski has accumulated 107 goals and 145 assists for 252 points.
Montreal drafted Grabovski in the fifth round (150th overall) of the 2004 NHL Entry Draft.
Kulemin, 27, collected nine goals and 11 assists for 20 points in 70 games with the Leafs last season.
The native of Magnitogorsk, Russia, has registered 84 goals and 111 assists for 195 points in 421 career NHL regular-season games, all with Toronto.
Kulemin was originally drafted by the Leafs in the second-round, 44th overall, of the 2006 NHL Entry Draft.