Morrow, who made $4.1 million last season, had 25 points (12 goals, 13 assists) in 44 games with Dallas and Pittsburgh last season. He added two goals and two assists in 14 playoff games with the Penguins.
Prior to joining Pittsburgh, Morrow had spent his entire 13-year career in Dallas, serving as the club's captain during the past seven seasons.
The six-foot, 210-pound native of Carlyle, Sask., has 249 goals, 293 assists and 1,222 penalty minutes in 850 career NHL games.
He has represented Canada internationally seven times and was part of the gold-medal winning team at the 2010 Vancouver Olympics.
Morrow, 34, was originally selected by Dallas in the first round, 25th overall, of the 1997 draft.