Cincinnati would get $500,000 from the Royals if Minor's mutual option for 2023 is declined, covering half the cost of the buyout.
The 29-year-old Garrett was 0-4 with a 6.04 ERA and seven saves in 63 appearances last season. Garrett was 6-3 with a 3.03 ERA in 90 appearances during the 2019-20 season.
The 34-year-old Minor went 8-12 with a 5.50 ERA across 28 starts with the Royals last season, but he was likely going to be pushed into a long reliever role if he stuck with Kansas City this season. The club is in the midst of a youth movement in the starting rotation, and Minor did not appear to fit with those plans.
Minor is due $10 million this season in the second year of an $18 million, two-year contract. The deal originally included a $13 million club option for 2023 with a $1 million buyout, but the contract contains a provision converting it to a mutual option because of the trade.
Garrett is eligible for arbitration and likely will have a salary in the $2 million range.