The Jazz are hoping Clarkson can deliver a boost to their bench scoring.
Exum, the No. 5 overall pick in the 2014 NBA draft, has struggled to stay healthy during his career but has shown glimpses of his elevated draft stock.
Exum took to social media Tuesday to thank the Jazz and their fans.
"Utah, can't begin to explain how great the past 5 and a half years have been," he wrote in an Instagram post. "I would like to thank the Jazz and the fans for growing with me and always supporting me throughout the seasons. It will always feel like home there. Super excited and ready for the next chapter!"
The Jazz will also send second-round picks in 2022 (via San Antonio) and 2023 (via Golden State) to Cleveland. This was the NBA's first trade since the Houston-Oklahoma City deal that centered on Russell Westbrook and Chris Paul on July 11.
Clarkson arrives with a $13.4 million expiring contract. Exum has two years and $19.2 million left on his contract. The Cavaliers will create a $3.83 million trade exception, which they have one year to use, ESPN front-office insider Bobby Marks reported.
The Cavaliers plan to start uprooting veterans on the roster to gather more draft picks and young assets. Clarkson, 27, is averaging 14.6 points per game, including a season-high 33 points on 12-of-27 shooting in Friday's victory over Memphis.
The Cavaliers are projected to have more than $28 million in salary-cap space for free agency.
Cleveland general manager Koby Altman and Utah general manager Justin Zanik have a strong working relationship, which has included working together on three trades in the past three years. The Jazz acquired Kyle Korver for Alec Burks and two second-round picks in November 2018, and Utah and Cleveland worked with Sacramento on a three-way deal at the February 2018 deadline that included Cleveland trading Jae Crowder for Utah's Rodney Hood.