The 30-year old Yates appeared in 131 games in relief during the last two seasons. He is 6-12 in his career with a 5.15 ERA.
The 22-year-old Redmond is 22-21 in three minor league seasons. He was expected to be in the starting rotation at Double A Altoona this season.
The Pirates also designated infielder Josh Wilson for assignment, unconditionally released pitchers Byung-Hyun Kim and Juan Perez and reassigned infielder Jorge Velandia and pitcher Jaret Wright to minor league camp.
In addition, the Pirates selected Doug Mientkiewicz from Triple-A Indianapolis and added him to the 40-man roster.