Portland gets a starting caliber center on an expiring deal as it awaits Jusuf Nurkic's return from a serious leg injury.
Whiteside, 30, is under contract for one more season after exercising the $27.1 million player option on his deal two weeks ago. Leonard and Harkless are also in the final year of their contracts.
Whiteside averaged 12.3 points and a team-best 11.3 rebounds per game last season, appearing in 72 games and starting 53 of those. He also averaged only 23 minutes per game, and at times expressed his displeasure about not having a larger role.
For his career, Whiteside has averaged 13.4 points and 11.4 rebounds over parts of seven seasons with Miami and Sacramento. He led the NBA in blocks per game in the 2015-16 season, then led the league in rebounds per game the following season.
He's third on Miami's all-time blocks list behind Alonzo Mourning and Dwyane Wade, and fifth on the team's all-time rebound list behind Udonis Haslem, Mourning, Rony Seikaly and Wade.