The Heat did not disclose terms of the deal, but agent Greg Lawrence told ESPN that it was a four-year, $50 million-plus contract.
Olynyk is the floor-spacing big man that Miami coach Erik Spoelstra had been determined to find this summer, an ideal complement to the Heat's frontcourt. His role could well expand with the Heat, whose player development program could be a boon to further growing Olynyk's game.
"As soon as Kelly Olynyk became an unrestricted free agent, we pursued him," Heat president Pat Riley said in a statement. "He is not only a post player, he can also play away from the basket. What we like the most is that he is a playmaker, tough defender and rugged rebounder.
"At just 26 years old, he fits in perfect with our young core that will play together in their primes."
In a move to clear salary-cap space, the Heat on Friday sent injury-prone power forward/center Josh McRoberts, a 2023 second-round draft pick and cash considerations to the Dallas Mavericks for center AJ Hammons.
McRoberts is due $6 million this season, the final year of his contract. Hammons, a second-round pick last year, has guaranteed salaries of $1.3 million and $1.5 million the next two seasons.
Celtics guard Jaylen Brown was complimentary of his now former teammate.
"I thought he probably should have gotten a little bit more money but you know how that goes," Brown said. "He probably should have been starting, he is a starter but he came off the bench for us and he played really well all year on a good team so I'm happy for Kelly. Miami has a good team and I wish him nothing but the best."
Brown said Olynyk's easy-going personality will be missed in Boston's locker room and noted how Olynyk stepped up in a big spot with a 26 points in the Celtics' Game 7 triumph over the Wizards in the conference semifinal.
Olynyk averaged 9.5 points, 4.8 rebounds in 20 minutes a game for the Celtics in 2016-17. He played four seasons for the Celtics after being drafted with the 13th overall pick in the 2013 NBA draft.
ESPN's Chris Forsberg contributed to this report.