When he was seven, his parents Michael and Fidelma Murray sent him to the Billie Barry and within five weeks he landed a Tesco television ad. Within two months he was in his first film, acting alongside Aidan Quinn in This Is My Father (1998). He then joined the National Performing Arts School and had his breakthrough role in Angela's Ashes (1999). He also acted alongside Jane Seymour in Yesterday's Children (2000).

Murray has been in a relationship with Shannon McCaffrey Quinn since late 2020. The couple have a son, Cooper Devon Murray, born on 2nd January 2021.