Terms of the contract signed Friday were not disclosed.
He was the ninth overall selection in the 2003 draft.
The 304-pound Williams is expected to move in as an immediate starter alongside defensive tackle Chris Hovan. The Vikings will hold their first training camp workout on Saturday.
The team also reached an agreement with linebacker E.J Henderson, their second-round pick, but running back Onterrio Smith, their fourth-round selection, remains unsigned.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards