The 36-year-old Norstrom played 903 career NHL games, most of them in Los Angeles, where was a captain.
Five of Norstrom's seven career playoff points came in this year's trip to the Western Conference finals, the deepest postseason run for Dallas since 2000. The Stars were eliminated in six games by Stanley Cup champion Detroit.
"This wasn't a rash decision by any means, and I'm comfortable with it," Norstrom said Tuesday. "I knew going into the season that this was the last year of my contract, and I didn't want to make a big distraction out of it."
Norstrom spent parts of three seasons with the Rangers before getting traded to the Kings in 1996. After 10 seasons in Los Angeles, Norstrom was acquired by Dallas at the trade deadline in 2007.
He played briefly for a team in his native Sweden during the lockout that wiped out the 2004-05 NHL season.