Rondo, 32, averaged 8.3 points, 8.2 assists and 4.0 rebounds per game last season for the New Orleans Pelicans.
According to Ramona Shelburne, Randle asked the Lakers to renounce his rights upon the Rondo signing once it became clear he would have a diminished role.
A Randle-Davis pairing will work similar to the Cousins-Davis pairing last season. A player option in the second year is included.
The Lakers will open training camp in September, and the competition between Ball and Rondo undoubtedly will be fierce.
Rondo, 32, was a member of the Celtics team that won the National Basketball Association championship in 2007-08, beating the Lakers in six games in the Finals.
Paul George Re-Signs With Thunder, Gets Max Contract
Oklahoma City could face the largest tax bill in National Basketball Association history, according to ESPN . The hope here is that Oklahoma City is able to somehow overcome last season's struggles.
Trump narrows Supreme Court list, to name nominee July 9
Elizabeth Warren (D., Mass.) said Trump was not a "king" and any nominee had to go through the U.S. Trump has made his intentions and vision for the United States very clear from the beginning.
France vow to end Lionel Messi's World Cup dreams
Do you think Argentina can beat France this weekend? "'Plan' is a big word, but of course we will try to limit his influence". Lloris refused to be drawn on comparisons between the talismanic Messi and France's prodigious winger Kylian Mbappe.
LeBron James' decision to join the Lakers marked an excellent start to Magic Johnson's plan to turn Los Angeles into a contender. The four-time All-Star also won a championship in 2008 with the Boston Celtics.
The Lakers have made another big move this offseason.
Deng's $36 million salary would then be paid out over five seasons.
By renouncing their rights to Randle, the Lakers parted ways with their longest-tenured player.
Randle was drafted No. 7 overall in the 2014 NBA Draft by the Lakers and has played every season of his professional career in Hollywood.
He has career averages of 13.5 points and 8.9 rebounds in 238 National Basketball Association games (182 starts).