Kennedy started 30 games for the San Diego Padres in 2015, posting a record of 9-15 with a 4.28 ERA. The right-hander has also spent time with the New York Yankees and Arizona Diamondbacks.
The 31-year-old's best season was with the Diamondbacks in 2011 when he went 21-4 and pitched to a 2.88 ERA. He ended up finishing fourth in National League Cy Young voting that year.
Kansas City is coming off a World Series title and needed to find a way to replace the departed Johnny Cueto in the rotation.