MLB.com reports that Rzepczynski will get $1.5 million with $500,000 in incentives for a potential $2 million if he makes the big-league team.
Nolasco, 36, has not pitched in the major leagues since 2017 with the Los Angeles Angels. He was released by Kansas City in spring training last year after allowing eight runs, five hits and three walks over 3 2/3 innings in one start and one relief appearance.
Nolasco is 114-116 with a 4.56 ERA in 312 starts and 18 relief appearances over 12 big league seasons.
Rzepczynski, 33, had a 6.97 ERA in 23 games last year with Seattle and Cleveland, allowing 11 runs -- eight earned -- 16 hits and 10 walks over 10 1/3 innings in 23 relief appearances, He is a 10-year big league veteran, primarily as a reliever.
Arizona announced the moves Friday.
Information from The Associated Press was used in this report.