The deal includes a club option for 2022 that, if exercised, can bring the total value to $24 million, the source said.
Miley, 33, went 14-6 with a 3.98 ERA and 140 strikeouts for the Houston Astros during the regular season, but he tailed off badly down the stretch and -- after making just one appearance during the American League Division Series -- was left off the rosters for both the AL Championship Series and the World Series.
Miley got off to a sizzling start in 2019, going 7-4 with a 3.28 ERA over 18 starts to earn All-Star consideration. However, after the break, his ERA ballooned to 5.07 over 15 outings, including a stretch in which he allowed 21 runs over 11⅓ innings in his final five regular-season appearances in September.
Also armed with a curveball, Miley has relied mostly on a cutter/changeup profile over the past two seasons, with hitters swinging and missing at nearly 18% of the changeups he threw. He has proved to be durable, not missing a start since July 12, 2018. And since the start of that season, he has thrown 248 innings with a 3.52 ERA.
After pitching for five teams over five seasons, Miley joined the Milwaukee Brewers in 2018 on a minor league deal and finally had a breakout season after tweaking his delivery and focusing on using his cut fastball. Despite missing almost three months because of injuries, Miley posted a career-best 2.57 ERA in 16 starts with the Brewers before entering free agency and signing a one-year, $4.5 million deal with the Astros.
The move to Cincinnati reunites Miley with his former pitching coach in Milwaukee, Derek Johnson. Miley joins a Reds starting rotation that includes Luis Castillo, Trevor Bauer, Sonny Gray and Anthony DeSclafani
Miley made his only All-Star Game appearance as a rookie for the Arizona Diamondbacks in 2012, when he won 16 games and was runner-up to Bryce Harper in Rookie of the Year voting. Overall, he is 85-82 with a 4.23 ERA in 249 appearances in his career, including 245 starts. He also has pitched for the Baltimore Orioles, Seattle Mariners and Boston Red Sox during his career.
ESPN's Keith Law contributed to this report.