"I am pleased to welcome Lou to the Laker family," General Manager Mitch Kupchak said of the 28-year old guard, in a statement. "We look forward to his contributions both on-court in bolstering our guard rotation, and also for the veteran leadership he can provide to our young players in the locker room."
The Lakers also signed second-round pick Anthony Brown, the team's 34th overall selection in June, to a multiyear deal.
The contract terms for the 6-foot-7 guard/forward have yet to be released.
Williams, who averaged 15.5 points a game last season with the Raptors, originally was drafted by the Philadelphia 76ers in 2005 with the 45th overall pick.
Brown scored 14.8 points a night at Stanford, shooting 44.1% from three-point range.