The team announced the signing Thursday. Terms were not disclosed. Williams, a forward-center out of Texas A&M, was selected 27th overall last month with the Celtics' lone draft pick.
Williams' signing comes days after he received a lecture from the team about accountability following a pair of off-the-court incidents. The 20-year-old slept through a scheduled conference call with reporters the day after the draft and then failed to catch a flight from his native Louisiana to Boston in time for a summer league practice.
Williams will wear jersey No. 44.
Boston signed free agent guard Brad Wanamaker earlier this week.