The teams announced the deals Wednesday.
Olynyk was a first-round draft choice last season who averaged 8.7 points and 5.9 rebounds in his first 70 NBA games. Sullinger was a 2012 first-round pick who is averaging 10.5 points and 7.3 rebounds in his career.
Zeller has career averages of 6.9 points and 4.9 rebounds. He was originally selected 17th overall by Dallas in 2012. The Celtics acquired him this year from Cleveland as part of a three-team trade.