A source told ESPN.com's Pierre LeBrun that the deal is worth $29.75 million -- an average of $4.25 million per season.
"John is a very special player, possessing a creativity and skill level that few in this League can match," Stars general manager Jim Nill said in a statement. "He fits in perfectly with where our core is at age-wise and his impact on our team was felt immediately. We expect him to build off of his rookie season and continue his development towards becoming an elite all-around defenseman."
The 22-year-old Klingberg had 11 goals and 29 assists in 65 games this season. Among all rookies, he finished fourth in assists, seventh in points and seventh in even-strength points (28). The Swedish native was selected by the Stars in the fifth round (131st overall) of the 2010 NHL draft.