Williams enjoyed a highly successful year with the Toronto Raptors last season as he averaged a career-high 15.5 points to go with 1.9 rebounds, 2.1 assists and 1.1 steals.
The 28-year-old shooting guard admitted that he was uncertain about whether he would be the same player after he tore his ACL in January 2013. But, fast forward more than two years later and Williams has thrived in a new environment after the Atlanta Hawks traded him to the Raptors.
Williams, who became a fan favourite in Toronto in a short space of time, will now be part of the Lakers' guard rotation, which currently includes Kobe Bryant, Jordan Clarkson, Nick Young and D'Angelo Russell, who they picked second in this year's NBA Draft.
Williams' agreement to move to Los Angles comes just a day after the Lakers negotiated a trade to acquire center Roy Hibbert from the Indiana Pacers.