Williams, 28, was the NBA's sixth man of the year last season while averaging a career-high 15.5 points for Toronto.
He provides instant offense off the bench and gets to the free-throw line with regularity. He is more of a scoring guard than passing guard, averaging 2.9 assists per game in his career.
They added Williams on Sunday and acquired shot-blocking center Roy Hibbert from Indiana on Saturday for a second-round draft pick. They also agreed to undisclosed terms with veteran power forward Brandon Bass.
Williams suffered a torn ligament in his right knee in January 2013 while with Atlanta. He sat out the start of the 2013-14 season but showed no signs of the knee slowing him down last season.
"I didn't think I was going to be the same player," Williams told reporters in April after winning the sixth-man award. "I knew I wasn't going to have the foot speed I once had, I knew I wasn't going to be able to jump as high. But it taught me to be smart and I worked on different parts of my game. Being able to evolve and change my game to win this award is very gratifying."
Williams has a slight build and is listed at 6 feet 2. He has started only 54 of 634 games.
The Lakers will mix in the 10-year veteran with promising combo guard Jordan Clarkson and recent draftee D'Angelo Russell, a point guard out of Ohio State. They also have Kobe Bryant, of course, returning for a 20th season, though he might play more at small forward.
The Lakers might not have quite enough cap space to acquire Hibbert and Williams, given the NBA's most recent projection of a $67.1 million salary cap next season.
The cap, though, might actually rise to about $69 million, according to cbssports.com. If so, the Lakers would be able to accommodate Williams and Hibbert, including the $2.3-million bonus the Indiana center was eligible to receive as a trade kicker. If the salary cap doesn't jump, the Lakers might need to clear additional space, perhaps trading Nick Young, Ryan Kelly or Robert Sacre.
Hibbert also has the ability to affect the cap situation. If the seven-year veteran is willing to waive his trade bonus, the Lakers might be able to time their moves to make everything fit just perfectly within their available space.
Perhaps complicating matters was the agreement with Bass, 30, who averaged 10.6 points and 4.9 rebounds last season with Boston, his 10th in the NBA.
After using their available cap space on Hibbert and Williams, the Lakers have an additional $2.8 million to spend via the team's "room exception." If that's not enough for Bass, moving out additional players via trade would be a requirement.
Another factor in the Lakers' fluid financial situation is the Dallas Mavericks' interest in free agent Jeremy Lin, who played one season with the Lakers. Dallas guard Monta Ellis has agreed to join the Indiana as a free agent, opening up the possibility of a multi-team deal with Ellis going to the Pacers via sign and trade, with Lin going to Dallas and the Lakers getting an unspecified asset in return.
Bresnahan is a Times sports writer. Pincus is a Times correspondent.