Heyman was born in London. He is the son of John Heyman, Producer of the films The Go-Between and Jesus, and Norma Heyman (née Parnell), an Actress, and Academy Award-nominated Producer of the films Dangerous Liaisons and Mrs Henderson Presents. His paternal grandparents were German-Jews who left Nazi Germany and emigrated to England prior to World War II, while his mother's family was English. He went to Westminster School and, following graduation, he decided to study abroad. He earned a degree in Art History from Harvard University in the U.S. in 1983.
Heyman started in the film industry as a production assistant on David Lean's A Passage to India, and in 1986, Heyman became a creative executive at Warner Brothers. In the late '80s, he became vice President of United Artists and subsequently embarked on an independent producing career with his first film, Juice, in 1992, followed by the cult "stoner" film The Stoned Age (1994) and others.
In 1997 Heyman returned to London and founded his own production company, Heyday Films. He has since produced a number of films including the popular Harry Potter film adaptations, beginning with 2001's Harry Potter and the Philosopher's Stone and ending with 2011's Harry Potter and the Deathly Hallows – Part 2. Other notable productions during this time include the 2007 blockbuster I Am Legend and the 2008 films The Boy in the Striped Pyjamas, Is Anybody There?, and Yes Man.
Heyman is also currently developing projects with Potter Director David Yates and has long been developing a film adaptation of Mark Haddon's 2003 novel The Curious Incident of the Dog in the Night-Time with Potter Screenwriter Steve Kloves.
After finishing work on the Harry Potter films, Heyman reunited with Harry Potter and the Prisoner of Azkaban Director Alfonso Cuarón to produce the 2013 space thriller Gravity starring Sandra Bullock. The film grossed more than US$700 million worldwide and was nominated for 10 Academy Awards including Best Picture. He also produced the 2013 comedy We're the Millers and the 2014 family film Paddington, for which he was nominated for the Alexander Korda Award for Best British Film.
It was announced in 2016 that Heyman is partnering with China's Ali Baba to produce a movie about Warrior Cats, feral cats who have a complex social hierarchy and take residence in a forest. The release date for the film is yet to be announced.
