Major League Baseball made the announcement on Wednesday.
Carrasco won the American League award. He was diagnosed with chronic myeloid leukemia in early June, missed three months while undergoing treatment and returned to the Indians in a relief role in September.
In October, the 32-year-old right-hander from Venezuela won the Roberto Clemente Award, presented annually by Major League Baseball to recognize a player's high character, community involvement and positive contributions.
Donaldson won the National League honor. He played only 52 games for Toronto and Cleveland in 2018 because of injuries, but bounced back for a big year with the Braves.
The 2015 AL MVP hit 37 home runs and had 94 RBIs for the NL East champions. Donaldson became the second straight Braves player to win the NL comeback award after pitcher Jonny Venters last year.
The award winners were chosen by the 30 team beat writers for MLB.com.