All three players received non-guaranteed training camp deals.
Brown, 22, is 7-foot-2 and finished last season with the Cavaliers after starting with the Mavericks. He averaged 4.3 points and 3.4 rebounds in 40 games overall.
Meanwhile, the Clippers lost Isaiah Hartenstein to the Knicks and have been seeking some help in the pivot.
Heading into free agency, Brown reportedly had also been drawing interest from the Rockets, Raptors and a few others. He has also spent time with the Trail Blazers and Thunder since entering the NBA in 2019.
Moon, 27, is 6-2 and appeared in 10 games with the Clippers on a two-way deal. He averaged 18.7 points, 4.6 rebounds and 6.5 assists in 21 games in the G League.
Scrubb, 21, is 6-5 and has been with the Clippers on a two-way deal for the past two seasons. He played 18 games for LA last year.
The Clippers have a roster spot available, and all three players are expected to compete for that job, as well as the two two-way spots.