Williams and Smith also were fined an additional two game checks, according to separate statements released by the league, for testing positive for the banned diuretic StarCaps.
NFL Network's Albert Breer reported Friday that the two other players who tested positive -- free-agent defensive linemen Charles Grant and Pat Williams -- also received the same punishment.
The suspension of Smith and Williams begins Saturday, Sept. 3, and they will be eligible to return to their teams' active rosters Monday, Sept. 19, following Week 2 games.
The St. Paul Pioneer Press first reported last week that Williams, 31, would face a reduced suspension, citing two people with knowledge of the situation. A union official told the newspaper that the new collective bargaining agreement created a more nuanced penalty system that helped Williams.
Instead of the automatic four-game suspension under the previous CBA, the NFL and NFL Players Association will implement a two-tiered system of discipline -- two-game suspensions for testing positive for diuretics and six games for testing positive for steroids.
According to the Pioneer Press, Williams, who's scheduled to make roughly $6 million in base salary this season, will lose approximately $1.4 million dollars for the four game checks missed.
Smith and his former teammate Grant tested positive for the same substance, but they weren't involved in the Minnesota lawsuit filed by Kevin Williams and ex-teammate Pat Williams.
Kevin Williams and Pat Williams initially were suspended four games in 2008 for using StarCaps, which contained a banned diuretic that can mask the presence of steroids. The players waged a long fight against the suspensions through federal and state courts, and the league allowed them to play pending a final resolution of the case.
The Williamses, who never were accused of taking steroids, said they didn't know StarCaps contained illicit substance bumetanide, which wasn't listed on the label.
Kevin Williams gave up the fight to avoid suspension in March because he was tired of the litigation, his attorney told The Associated Press. In April, the Minnesota Supreme Court cleared the way for the NFL to suspend Pat Williams by declining to consider his appeal of a decision that had gone against both him and Kevin Williams.
The suspension could help Kevin Williams, who's dealing with a painful case of plantar fasciitis in his left foot. Taking the first two weeks of the season off could give it more time to heal, even though Williams said this week that he expected to play through pain all season.
There is no question that Williams' absence is a big blow to the Vikings' defense. The former All-Pro is the anchor of the defensive line and one of the most versatile players at his position in the game, excelling both at stopping the run and rushing the passer.
The case was watched by other major sports leagues -- including Major League Baseball, the NBA and the NHL -- that supported the NFL and said their drug-testing programs would be at risk if players were allowed to challenge drug-testing policies in state courts. The NFL argued its anti-doping policy was a product of its collective bargaining agreement with the players' union and was governed by federal law.
The Associated Press contributed to this report.