The St. Paul Pioneer Press reported Sunday the deal has more than $13 million in guaranteed money, which will make the 26-year-old Williams the NFL's highest-paid defensive tackle.
"I'm excited to get a deal done and finish my career with the team that drafted me," Williams said.
"Kevin has been productive as an interior player on the defensive line," said Vikings Coach Brad Childress on the team's Web site.
After a successful college career at Oklahoma State, he was a first-round pick in the 2003 NFL Draft.
In 15 games this season, the 6-foot-5 inch, 311-pounder has 33 solo tackles and five sacks, and is regarded as one of the league's best run-stoppers.
He was chosen for the Pro Bowl for the second time, where he will be an NFC starter.
Notable deaths of 2014 [PHOTOS]