Benn succeeds Brenden Morrow, the Stars captain from 2006 until getting traded to Pittsburgh last March.
Nill says the 24-year-old Benn has "in a very short period of time" gone from being an exciting up-and-coming NHL player to a franchise cornerstone.
Benn has spent all four of his NHL seasons with the Stars. He led the team with 33 points (12 goals, 21 assists) in 41 games last season. He has 193 points in 263 career games, and was an All-Star in 2012.