Henderson began his Broadway career with a 1986 comedy revue starring Rowan Atkinson.
His Broadway credits include revivals of The Merchant of Venice (1989), Cat on a Hot Tin Roof (1990), Hamlet (1995), The Iceman Cometh (1999), The Real Thing (2000), Faith Healer (2006), and A Moon for the Misbegotten (2007), and the original productions of Indiscretions (1995), Copenhagen (2000), Decocracy (2004), Chitty Chitty Bang Bang (2005), and Deuce (2007).
He was involved in the refurbishment of the Royal Court Theatre and has designed for Madame Tussauds in London, New York City, and Las Vegas.
He also has designed tours for Eddie Izzard, Victoria Wood, French & Saunders, Ruby Wax, and Steve Coogan.
He has won the Laurence Olivier Award for Best Lighting Design five times out of nine nominations.