According to the Boston Herald, which first reported the deal, Turner will sign for a portion of the midlevel exception.
Boston is adding the 2010 No. 2 draft pick. The 25-year-old Turner will be looking to revitalize his career in Boston.
Turner has averaged 11.1 points, 5.3 rebounds and 3.1 assists over four NBA seasons. He was dealt from Philadelphia to Indiana at the 2014 trade deadline, with the playoff-bound Pacers looking to bolster their bench. Turner played only sparingly as a reserve, and Indiana was bounced in the Eastern Conference finals.
After the season, the Pacers did not extend an $8.7 million qualifying offer, which made Turner a free agent.
Boston has a growing crowd at the shooting guard and small forward positions. The team drafted Marcus Smart and James Young in June's draft and also re-signed starting shooting guard Avery Bradley to a four-year, $32 million extension this past offseason.
Boston will soon have 18 players on a roster with a payroll commitment of nearly $80 million. The team has three non-guaranteed deals, which could help it dip back below the luxury-tax line, but more moves are likely as the Celtics shape the roster before the start of the 2014-15 season.