The Kings also sent forward Konstatin Pushkarev and third-and fourth-round picks in 2007 to the Stars in exchange for a first-round pick in 2008, second-and third-round picks this year, defenceman Jaroslav Modry and defensive prospect Johan Fransson
Norstrom, 35, registered two goals and seven assists in 62 games for the Kings this season.
The six-foot-two, 210-pound Swede is the Kings' all-time leader in games played among defencemen (780) and he is the fourth overall in games played in franchise history.
He was also the 12th captain in club history and had worn the "C" for the Kings since the 2001-02 season.
"Mattias solidifies our defensive group and also adds character and veteran leadership to our locker-room," Dallas GM Doug Armstrong said in a statement. "He is an outstanding NHL defenceman and we are extremely happy to have acquired him today. We look for him to make an immediate impact on this hockey club as we push towards the playoffs."
Norstrom has 16 goals and 133 assists in his 823 career NHL games with the Kings (1996-2007) and the New York Rangers (1994-1996). The two-time all-star was the Rangers' second round (48th overall) in the 1992 NHL Entry Draft.
Norstrom is also a two-time Olympian for Sweden (1998, 2002). He was selected to play at the 2006 Winter Olympics but missed the tournament for health reasons.