Keuchel was the big winner in the American League with 22 first-place votes and 186 points in the Baseball Writers' Association of America voting.
Arrieta received 17 first-place votes and 169 points to come out on top in a much closer vote in the National League.
Keuchel, 27, posted a league-best 20-8 win record and had a 2.48 ERA with 216 strike-outs for the Astros, who made the play-offs for the first time since 2005.
"Something I definitely never expected," Keuchel, speaking on MLB Network, said. "Just playing the game was good enough for me."
Arrieta finished the regular season with a 22-6 record and a 1.77 ERA. He was unbeatable during the second half of the season, posting an 11-0 record with a 0.41 ERA in 12 starts beginning August 4 and pitching a no-hitter against the Dodgers on August 30.
Arrieta is the third Cubs winner of a major post-season award this year and the team's first Cy Young recipient since Greg Maddux in 1992.
The Cubs' Joe Maddon was named National League Manager of the Year and third baseman Kris Bryant was voted NL Rookie of the Year.