The deal is worth $38.5 million, and the option years are for $13.5 million and $14 million, a source told ESPN. The deal also also includes escalators based on Cy Young Award finishes from 2015-18 that could increase Kluber's salary in subsequent years and could potentially make his new deal worth $77 million.
"I wanted to be here. I wanted to be in Cleveland," Kluber said. "That was the driving force behind it for me."
Kluber, 28, enjoyed a major breakthrough in 2014, posting an 18-9 record with a 2.44 ERA and 269 strikeouts. He overtook Seattle's Felix Hernandez in the Cy Young race down the stretch and joined Gaylord Perry, CC Sabathia and Cliff Lee as the fourth Indians pitcher to win the award.
"This is an exciting day for our organization, Corey and his family," Indians general manager Chris Antonetti said in a statement. "In his time with us, Corey has grown into a leader in our clubhouse and an exemplary teammate. His tireless work ethic, consistent preparation and fierce competitiveness set an example for our younger players, and his presence on our team is a key reason that we are prepared to compete for a championship in 2015 and beyond."
Carrasco, a five-year veteran, is coming off a year in which he logged career bests with 134 innings, 140 strikeouts and a 2.55 ERA.
Kluber, who has only two years of major-league service time, agreed to a $601,000 contract with the Indians in mid-March. He was the last player on Cleveland's 40-man roster to agree to terms.
Information from The Associated Press was used in this report.