Rios was slated to earn $12.5 million in 2016, the option year on a one-year $9.5 million contract he signed last December.
Guthrie was in the last year of his three-year, $25 million contract that includes a $3.2 million buyout.
Rios played in 105 games this season, batting .255 with four home runs and 32 RBIs. The 12-year veteran had his best season with the Chicago White Sox in 2012, hitting .304 with 25 home runs and 91 RBIs.
Guthrie had an 8–8 record in 24 starts, posting a 5.95 ERA.