Tennant, who also hosted the ceremony, won for his work in Kafka: The Musical, written and composed by Murray Gold for BBC Radio 3.
Rosie Cavaliero won Best Actress for Katie Hims' Lost Property: A Telegram, which also was named best audio drama at the awards.
Tennant is best known for playing the title role in the BBC's Doctor Who series. Early in his career, he spent two seasons with the RSC, and recent stage roles include the title role in Hamlet and Benedick in Much Ado About Nothing.
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