DeGrom was looking to become the third pitcher in MLB history to win the award in three consecutive seasons.
The Reds had never had a Cy Young winner, making them one of four active MLB teams without a Cy Young winner and the only team founded prior to 1961 without one.
Bauer ended that drought.
He went 5-4 with an NL-best 1.73 ERA in 11 starts, helping the Reds reach the playoffs for the first time since 2013. Animated on the field and outspoken off it, the 29-year-old right-hander struck out 100 in 73 innings and led the majors with two shutouts, a pair of seven-inning performances on doubleheader days.
He became a free agent after the season and turned down the Reds' qualifying offer, but left the door open for a return.
"I haven't thought about free agency very much yet, to be honest,'' said Bauer, known for some unusual and progressive training methods that have helped turn him into one of baseball's best pitchers. "I have had a lot of stuff that I've been doing trying to get my offseason underway, trying to get better at baseball.''
This is the first Cy Young for Bauer, who tied for sixth in the AL voting in 2018, after he went 12-6 with a 2.21 ERA for the Indians. He was traded to Cincinnati at last year's deadline as part of a three-team deal that moved Yasiel Puig to Cleveland.
Bauer struggled after he was acquired by the Reds, going 2-5 with a 6.39 ERA in 10 starts. He returned to form when this season started in July. He gave up only two runs and eight hits in 26⅓ innings over his first four starts. He also closed out the season with a flourish, recording a 1.29 ERA and 46 strikeouts in 35 innings over five September starts.
"The biggest deal this year is I was just healthy," he said. "I was able to go out there and compete, be on a routine.''
Bauer pitched Game 1 of the playoffs at Atlanta and struck out 12 in 7⅔ innings. But the Reds lost 1-0 in 13 innings and failed to score during the Braves' sweep.
Bauer, who has his own YouTube account and nearly 400,000 followers on Twitter, was selected by Arizona with the No. 3 overall pick in the 2011 draft. He is 75-64 with a 3.90 ERA in 205 career games, including 195 starts.
The Associated Press contributed to this report.