The free agent was 9-11 with a 5.36 ERA in 30 starts for Cincinnati last season. The right-hander has made at least 30 starts in four of the past five years and is 68-60 with a 4.72 ERA for his career.
His best season was 2002, when he helped the Anaheim Angels win the World Series, going 15-9 with a 3.77 ERA. He went 6-0 over his final nine starts that season.
Also Thursday, the Nationals signed right-hander Tony Armas Jr. to a one-year contract.
Armas went 7-7 with a 4.97 ERA in 19 starts last season for Washington. The 27 year-old is 39-48 with a 4.32 ERA in 121 starts spanning seven seasons with the franchise.