Texas announced the moves Friday, a day after acquiring Castillo in a trade from the Chicago White Sox.
Castillo has an $8 million option and a $500,000 buyout. The 32-year-old catcher hit .209 over 72 games last season.
Kelley was 5-2 with 11 saves and a 4.94 ERA in 50 games, with two stints on the injured list. The 35-year-old Kelley had a $2.5 million option with a $250,000 buyout.
Jones, who has a $3.75 million club option with a $1.25 million buyout, was acquired in July from the White Sox while recovering from right forearm surgery. He had a 3.48 ERA in 13 relief appearances in Chicago before going on the injury list in April.