"It was something that (coach) Dave (Tippett) and I talked about," Stars general manager Doug Armstrong said. "We felt it was important for Brenden to take that leadership role going forward and it was important for the team."
Modano and veteran defenceman Sergei Zubov will serve as alternate captains.
The 27-year-old Morrow has spent his entire career in Dallas after being selected by them in the first round of the 1997 draft.
"This is an honour and a privilege," he said. "I realize how important it is to have a group of leaders that rally together to accomplish great things. I look forward to the challenges that lie ahead for this team and for me."
Morrow was the only player in the NHL last season to score more than 20 goals and serve more than 125 penalty minutes. He scored 23 times and assisted on 42 for a career-best 65 points, and his plus-30 rating was the best on the team.
It earned him a US$24.6-million, six-year contract extension this summer that will keep him in Texas until 2013. The native of Carlyle, Sask., loves being a member of the Stars.
"I really believe in this organization and the commitment they've made to me and to winning," he said.
In 451 career NHL games, Morrow has 120 goals and 149 assists for 269 points and 748 penalty minutes. He is the only current Dallas player who has posted three straight 20-goal seasons.