Terms of the deal were not released.
The Celtics traded up in last month's draft to pick Olynyk with the 13th overall selection. General manager Danny Ainge sent the No. 16 pick and two future second-rounders to the Dallas Mavericks to get Olynyk, who was fifth in voting for the Wooden Award. Olynyk averaged 17.8 points and 7.3 rebounds while leading Gonzaga to a 32-3 season.
Olynyk made his summer league debut on Sunday, scoring a game-high 25 points on 9-of-12 shooting in the Celtics' 95-88 loss to the Orlando Magic.
"Some shots fell early, which makes it easy for a player," Olynyk said of his debut. "Some teammates put me in a really good position to succeed, so I've got to thank them."
New Celtics coach Brad Stevens praised the rookie's performance.
"I thought he made plays off a bounce, he shot it freely, which is really a positive thing," said Stevens, who watched from the sidelines. "I don't want him to be reluctant at all shooting the basketball. He can pass for his size. He's good at so many things that would be a tough matchup at a big position."
Information from ESPNBoston.com's Chris Forsberg and The Associated Press was used in this report.