She was born to English parents in Cambridge, Massachusetts, United States, while her father was a visiting professor at MIT, but she grew up in Scotland. She thus holds dual US/UK citizenship.

She attended drama college and graduated from the Royal Academy of Dramatic Arts in London. After some promising work as an actress in the UK, She moved to the United States. She had met American writer/director David Mamet while acting in his play Speed the Plow during its run at The National Theater in London. She subsequently became his wife in 1991. She and Mamet have two children, Clara and Noah.

From 1986 to 1990 she was the lead singer of the British folk/pop band Ruby Blue. Pidgeon left Ruby Blue, shortly after the band had signed a major record label and was beginning to gather both commercial and critical success. She decided to concentrate on her acting career, starring in Mamet's plays and films, initially in the movie Homicide, then in the play Oleanna, a part written for her. After marrying Mamet, she has only acted in work that her husband has either written or directed.

Returning to music in 1994, she released the solo album The Raven, followed by New York Girls' Club. A further album, The Four Marys, a collection of traditional Celtic folk songs, followed in 1998.

In October 2005 she released Tough on Crime, which featured the late Billy Preston on keyboards.

Pidgeon is a convert to Judaism.

Growing up in Edinburgh, Rebecca was a teenage friend of singer Shirley Manson.