The two sides agreed to a one-year, $3.5 million deal.
Beasley, 29, is coming off a bounce-back 2017-18 season with the New York Knicks. In 74 games, he averaged 13.2 points and 5.6 rebounds while shooting 50 percent from the field and 40 percent from beyond the arc.
He was one of New York's most consistent players and will serve a vital role as one of the Lakers' key reserves.
The 6-foot-9 forward also had interest from the Oklahoma City Thunder, sources said.
Drafted second overall by the Heat in 2008, Beasley has averaged 12.7 points and 4.8 rebounds per game for his career.