Drummond announced the news Tuesday during his first meeting with reporters as a member of the Lakers.
Lakers head coach Frank Vogel confirmed that Drummond will play against the Bucks.
"We're gonna need 'em all," Vogel said. "There's no doubt in my mind that we're gonna need all three of them."
The Lakers signed Drummond to provide a boost as they wait for LeBron James and Anthony Davis to return from injuries as well as to provide depth in the frontcourt.
Davis was cleared by the team last week to advance his on-court work as he recovers from calf and Achilles injuries. The eight-time All-Star hasn't appeared in a game since Feb. 14.
Shams Charania of The Athletic and Stadium reported Thursday that James has a recovery timetable of four to six weeks from the time he suffered an ankle injury March 20.
Drummond averaged 17.5 points and 13.5 rebounds per game in 25 appearances for the Cavs this season.