The team had until Thursday to cut the 6-foot-10-inch Randolph or else his contract would have been fully guaranteed for the 2013-14 season.
Randolph's agent confirmed to the Globe that the Celtics informed Randolph that they won't be picking up the option on his non-guaranteed deal, thus ending his tenure with the team he joined in February after playing in China.
In 16 regular-season games with the Celtics, the 29-year-old Randolph, a former Duke standout, averaged 4.2 points, 4.4 rebounds, and 12.4 minutes.
But those numbers prorate to 17 rebounds per 48 minutes, good for the 16th-highest such output in the NBA during the 2012-13 season.
Randolph stood to make relatively little as compared with the $12 million Celtics forward Kris Humphries is owed next season.
But with the Celtics' desire to trim salary to stay under the tax line, and with a crowded roster especially heavy in the frontcourt with Humphries, Brandon Bass, Vitor Faverani, Jared Sullinger, Kelly Olynyk, and Fab Melo, Randolph was simply a victim of the numbers.
With Randolph off the books, the Celtics have 15 signed players -- the most a team can carry during the regular season -- with a salary commitment of about $72.5 million, which is still over the $71.75 million luxury tax line for the 2013-14 season.