He is the son of an actress turned schoolteacher, Jenny Davis, and of Patrick Dromgoole, a theatre director and television executive, whose directing credits included the first production of Joe Orton's Entertaining Mr. Sloane. Born in Bristol, Dromgoole grew up on a farm in Somerset and attended Millfield School in Street, Somerset. His sister is theatre and radio director Jessica Dromgoole. When he was 16, he formed his own theatre company which took shows to the Edinburgh festival and toured them round the south-west. He studied English and classics at Cambridge University, where he directed student productions.
Six months after graduating from Cambridge, Dromgoole started working part-time as an assistant director at the Bush Theatre, London. In 1990 he became artistic director of the Bush, and stayed there until 1996. During this time, he premiered 65 new plays including early works by Billy Roche, Philip Ridley, Catherine Johnson, Sebastian Barry, Jonathan Harvey, Helen Edmundson, Simon Bent, Naomi Wallace, Irvine Welsh, David Harrower, Samuel Adamson and Conor McPherson.
After a period in charge of new plays for Sir Peter Hall's company at the Old Vic, he ran the Oxford Stage Company (now known as Headlong) from 1999 until 2005. His directing credits during this time included Troilus and Cressida, 50 Revolutions, Anton Chekhov's Three Sisters, Rookery Nook by Ben Travers and August Strindberg’s Easter.
In 2005, he took over from Mark Rylance as artistic director of Shakespeare's Globe. In 2008, he signed a new three-year contract to continue in the role until 2011. At the Globe, he directed Coriolanus and Antony and Cleopatra for the 2006 season, Love's Labour's Lost for the 2007 season and King Lear in 2008. In January 2014 he directed The Duchess of Malfi, the opening production at the Sam Wanamaker Theatre (the Globe's indoor counterpart). In July 2013, Shakespeare's Globe announced that Dromgoole will leave the post on 23 April 2016.
His other directing credits include revivals of Someone Who’ll Watch Over Me at the New Ambassadors Theatre in London, Noël Coward's Present Laughter, with Rik Mayall, George Bernard Shaw's John Bull's Other Island at London's Tricycle Theatre, and Eric Schlosser's Americans at the Arcola Theatre. He has also directed plays in the US and Romania.
In 2000, his book The Full Room: An A-Z of Contemporary Playwriting provided a personal survey of contemporary British playwriting. In 2006, Will and Me: How Shakespeare Took Over My Life charted his fascination with William Shakespeare, and won the inaugural Sheridan Morley award. Dromgoole has also contributed to The New Statesman, The Sunday Times and other publications.
- Times: Dominic Dromgoole (2008)
- Independent: Dominic Dromgoole (2008)
- Interview Part I (2004)
- Interview Part II (2004)
- Shakespeare's Globe online
- Old Vic Theatre, London