Murphy attended the Presentation Brothers College, Cork, and later studied law at University College Cork (UCC). Initially his interest in performing was led by music. He played guitar with a Frank Zappa influenced band called . However, by the time he left college his primary interest was acting. His first major role was in the UCC Drama Society production of was Murphy's first big break. He was cast in the central role of Pig in Corcadorca's 1996 production of Enda Walsh's original play. He later reprised that role for the 2001 feature film version by Kirsten Sheridan. Also, he wrote and sang the song became 2003's sleeper hit in the USA that the bigger studios and directors started to take notice.

In recent years he has had smaller parts in such Hollywood films as . 2005 was the year that brought Murphy into more reknown with his acclaimed performance as Dr. Jonathan Crane (aka The Scarecrow) in , co-starring Rachel McAdams as his would-be victim.

He originally auditioned for the role of Bruce Wayne and Batman in . Christopher Nolan was reportedly impressed with his audition; while he decided to give Christian Bale the lead role, he persuaded Murphy to play Dr. Jonathan Crane (aka The Scarecrow).

Currently, he stars in the movie , based on the novel of the same title by Patrick McCabe. He has received outstanding reviews, and he is nominated for a Golden Globe for Best Actor in Musical and Comedy in this movie.

Murphy married his long term girlfriend, Irish-born Yvonne McGuinness (b. 1972), in August 2004 in Provence, France. They recently had a son, who they named Malachy, and they currently reside in London, England.

According to magazine, he was #3 of "The Most Valuable Players of Summer 2005", a list for entertainers who have outstanding breakthrough performances for the year 2005. He was placed behind Terrence Howard and Matt Dillon. The magazine went on to compare him with Robert Mitchum.