The deal runs for three years, includes club options in 2019 and 2020 and close to $22 million in guaranteed money, according to Passan.
Carrasco posted a 2.55 ERA with 140 strikeouts and 29 walks over 134 innings last season. In two starts this spring, Carrasco recorded a 2.70 ERA and yielded two earned runs over 6 2/3 innings.
The 28-year-old has spent all five seasons of his career in Cleveland.
The Indians open the 2015 season on Monday against the Houston Astros.