The Los Angeles Clippers opened a starting position for No. 1 pick Blake Griffin on Wednesday.
The trade can't be finalized until the league establishes the salary cap July 8 and lifts the moratorium on player movement.
The Clippers acquired Randolph from the Knicks last November to fill the void left by Elton Brand signing with the Sixers. Randolph averaged 20.9 points and 9.4 rebounds per contest in 39 games for Los Angeles. A knee injury cost him time, however, and the Clippers limped to the worst record in the league.
On draft night, the Knicks traded Richardson to the Grizzlies for center Darko Milicic. Richardson won't play a game for Memphis. The nine-year veteran averaged 10.2 points and 4.4 rebounds last season. He now returns to the team that drafted him in the first round of the 2000 draft.