Randle was set to be a restricted free agent. The Lakers will be his fifth team in as many seasons.
With Randle gone, the Lakers now have $5 million in cap room.
Deng's $36 million salary would then be paid out over five seasons.
A Randle-Davis pairing will work similar to the Cousins-Davis pairing last season.
Rondo was excellent in the playoffs as the Pelicans swept the Portland Trail Blazers in the first-round of the Western Conference playoffs.
The Lakers came to an agreement with free-agent star LeBron James on Sunday and have been active in free agency, coming to terms with guard Kentavious Caldwell-Pope, center JaVale McGee and guard Lance Stephenson.
Despite losing Randle's defensive abilities, the Lakers have managed to upgrade their defense in the past 48 hours.
Rondo is on his sixth team since the 2014-15 season and has often been disengaged on the court, accused of assist-hunting, and his defense is mostly overrated.
Fiesty guard Rajon Rondo is heading to the LA Lakers. Depth was a concern at the position. He's led the National Basketball Association in assists three times over his career, averaging north of 11 assists per game in those campaigns.
The 32-year-old most recently played for the New Orleans Pelicans and has proven to been one of the best passing point guards of his generation.
Information from ESPN's Ohm Youngmisuk, Ramona Shelburne and Bobby Marks was used in this report.