Arroyo, who turns 39 next month, and the Nationals agreed to a minor league contract Tuesday with an invitation to major league spring training.
Arroyo, a 2006 NL All-Star with the Cincinnati Reds, became a free agent in November when the Los Angeles Dodgers declined a $13 million club option and paid a $4.5 million buyout. The Dodgers acquired him from the Atlanta Braves as part of a three-team deal at the July 31 trade deadline.
In his most recent big league action, Arroyo was 7-4 with a 4.08 ERA in 14 starts for the Arizona Diamondbacks in 2014. Across 15 years in the majors with four clubs, Arroyo is 145-131 with a 4.19 ERA.