It's reportedly a two-year contract, according to The Athletic's Shams Charania.
The former No. 2 overall selection in the 2014 draft should provide Boston with scoring firepower in the frontcourt. Parker has averaged 14.8 points during his seven-year career.
Boston is waiving Moritz Wagner in a corresponding move.
Parker has battled injuries throughout his NBA career, tearing his left ACL on two separate occasions and more recently dealing with back and shoulder issues.
The Celtics currently sit fifth in the Eastern Conference with a 30-26 record.