The Angels announced their decisions Tuesday night, saving about $6 million in salary commitments for next season.
Beckham earned $4,175,000 this year and likely would have received a raise to about $5 million in arbitration, more than the Angels wanted to pay for a probable backup infielder. Los Angeles acquired Beckham from the White Sox on Aug. 21, and general manager Jerry Dipoto has said the club would be interested in keeping him for less money.
LeBlanc was a fill-in starter for the injury-troubled Angels down the stretch. He was waived by the club in June before returning.