Randolph's $1.1 million salary would have been guaranteed if the Celtics did not waive him by the end of the day Thursday.
The Celtics' roster now stands at the regular-season limit of 15 players, all of whom have guaranteed contracts. Those players account for roughly $72.5 million in salary, slightly over the luxury-tax threshold of about $71.75 million.
Second-round draft pick Colton Iverson remains unsigned but appears set to sign in Turkey if Boston can't find space for him.
Imported from China late last season with Boston thin on big men, Randolph revitalized his NBA career by being a relentless rebounder in limited on-court opportunities. Over 16 regular-season appearances, Randolph averaged 4.2 points and 4.4 rebounds over 12.4 minutes. He grabbed 26.3 percent of all available defensive rebounds during his time on the floor and 22.4 percent of all caroms overall, which were the best numbers on the team, albeit in a small sample size of 198 minutes. When the Knicks went small in the playoffs, Randolph appeared for just three minutes in one game but managed to grab three rebounds in that minuscule span.