Randle, a 6-9 big man, averaged a career-high 16.1 points along with eight rebounds and 2.6 assists per game last season while playing in all 82 games.
Randle had been searching for an offer sheet as a restricted free agent, but the Lakers didn't want to match a sheet and commit long-term years and money as they pursue the possibility of star free agents in 2019, including Kawhi Leonard of the San Antonio Spurs.
Randle came into training camp last season in the best shape of his life.
As the Lakers continue to reshape their roster around LeBron James - keeping maximum flexibility going forward, although putting together an interesting mix of players that lack shooting - the Lakers made two fast moves Monday afternoon. Players and teams are free to negotiate and agree on new contracts, but they can't officially sign them until Friday morning PT.
LeBron James Joins the Lakers: Kobe Bryant, Chrissy Teigen, More React
Maybe age plus the toll of four incredibly long seasons catches up to the Warriors next season, and they begin a regression. The Klutch tweet had ESPN's Adrian Wojnarowski beat by three minutes because, well, it was the original source.
Rondo is the second notable former Celtics point guard to join this current Lakers team, joining Isaiah Thomas, who was traded from the Cleveland Cavaliers this past season. Randle is more of a ball-handler and off-the-dribble threat.
Deng's $36 million salary would then be paid out over five seasons.
DeMarcus Cousins has been mentioned as a possibility for the Lakers, who might be interested in bringing him in.
Randle, 23, was originally drafted by the Lakers with the seventh overall pick of the 2014 draft.
Despite his development on offense, Randle started only 49 games while averaging 26.7 minutes.