The Indians subsequently signed Leon to a one-year, $2 million deal, avoiding arbitration.
Cleveland sent minor league right-hander Adenys Bautista to Boston on Monday for Leon, 30, who has split his eight-year major league career between Boston and Washington. Leon batted just .192 last season in 65 games for the Red Sox, but he's been ranked among the American League's best defensive catchers.
To make room on their roster, the Indians designated right-hander James Hoyt for assignment. The club also chose not to tender a 2020 contract for catcher Kevin Plawecki, who last season served as Roberto Perez's primary backup -- a role that could now go to Leon.
A switch-hitter, Leon has a .221 career batting average with 25 home runs and 123 RBIs in 392 games. When he's been behind the plate, Boston's pitchers have posted a 3.74 ERA.
Bautista, 22, went 1-1 with a 7.79 ERA in 14 relief appearances for the Indians in Arizona Rookie League in 2019.
Boston did tender outfielder Jackie Bradley Jr. a contract for the 2020 season, preserving their rights to him. The move means the sides can continue to negotiate or go to arbitration.
The Bradley decision was closely watched because the team has said it would like to shed about $30 million in payroll to get under baseball's luxury tax threshold. To do so, it might now have to trade 2018 AL MVP Mookie Betts.
Bradley batted .225 last season while leading the AL in assists and putouts for a center fielder. He is projected to earn about $10 million next season.
Information from The Associated Press was used in this report.