Boudin was born in New York City to Jewish parents.[4] His parents, Kathy Boudin and David Gilbert, were Weather Underground members, both convicted of murder.[5]

When Boudin was 14 months old, his parents were arrested for murder in their role as getaway car drivers in the Brink's robbery of 1981 in Rockland County, New York.[4][6] His mother was sentenced to 20 years to life[7] and his father to 75 years to life for the felony murders of two police officers and a security guard.[8] After his parents were incarcerated, Boudin was raised in Chicago by adoptive parents Bill Ayers and Bernardine Dohrn, who, like his parents, had been members of the Weather Underground.[9] Boudin reports that he did not learn to read until age 9.

Boudin descends from a long left-wing lineage. His great-great-grand-uncle, Louis B. Boudin,[12] was a Marxist theoretician and author of a two-volume history of the Supreme Court's influence on American government, and his grandfather Leonard Boudin was an attorney who represented controversial clients such as Fidel Castro and Paul Robeson.[13] His uncle Michael Boudin[12] is a judge on the United States Court of Appeals for the First Circuit, and Michael Boudin's uncle Isidor Feinstein Stone was an independent journalist.

Before law school, Boudin traveled to Venezuela and served as a translator in the Venezuelan Presidential Palace during the administration of Hugo Chavez.

Boudin translated Understanding the Bolivarian Revolution: Hugo Chávez Speaks with Marta Harnecker into English,[24][25] co-edited Letters from Young Activists: Today's Young Rebels Speak Out,[26] and co-wrote The Venezuelan Revolution: 100 Questions – 100 Answers.[27] His latest book, Gringo: A Coming of Age in Latin America, was released in April 2009 by Charles Scribner's Sons.