Williams, whose signing was announced by general manager Mickey Loomis on Friday, is entering his 13th NFL season.
The 6-foot-5, 311-pound lineman was a 2003 first-round draft choice by Minnesota, with whom he spent his first 11 seasons. Williams moved to Seattle last season, during which he was credited with 29 tackles, including three sacks. He also started all three of the Seahawks' postseason games.
During his career, Williams has been credited with 495 tackles, 63 sacks, eight forced fumbles, 13 fumble recoveries and five interceptions. He also has been chosen to six Pro Bowls.
New Orleans waived tight end Harold Spears, an undrafted rookie out of New Hampshire.