Byrne, the first of six children, was born in Dublin, Ireland, the son of a cooper and a hospital worker. Byrne was raised Catholic and educated by the Irish Christian Brothers. Despite spending five years of his childhood in a seminary training to be a priest, he said in an interview, "I spent five years in the seminary and I suppose it was assumed that you had a vocation. I have realized subsequently that I didn't have one at all. I don't believe in God. But I did believe at the time in this notion that you were being called." He attended University College Dublin, where he studied archaeology and linguistics, becoming proficient in Irish. He played football in Dublin with the famous Stella Maris Football Club in Drumcondra and has fond memories of his time spent there.

Byrne worked in archaeology when he left UCD, but maintained his love of his language, writing the first drama in Irish, Draíocht, on Ireland's national Irish television station, TG4, when it began broadcasting in 1996.

He discovered his passion for acting later in his life. Before becoming an actor, Byrne worked at everything from an archaeologist to a cook, a bullfighter, and a Spanish schoolteacher. When he finally found acting, aged 29, he began his career on stage with the Focus Theatre and the Abbey Theatre in Dublin, later joining the Royal Court Theatre and the Royal National Theatre in London.

The actor came to prominence on the final season of the Irish television show The Riordans, subsequently starring in his own spin-off series, Bracken. He made his film debut in 1981 as Lord Uther in John Boorman's classic King Arthur epic, Excalibur. After that, he starred in numerous films such as: Gothic, Lionheart, Siesta (on the set of which he met his future wife, Ellen Barkin), Miller's Crossing (this film was chosen by Time magazine in 2005 as one of the 100 greatest films ever made), Shipwrecked, Into the West, The Usual Suspects, The Last of the High Kings, The Man in the Iron Mask, Enemy of the State, Stigmata, End of Days (where he went from playing a priest in Stigmata to Satan in the same year), Ghost Ship, Vanity Fair, Leningrad.

Byrne currently stars as therapist Dr. Paul Weston in the new, critically acclaimed HBO primetime weeknight series In Treatment. He has recently been coined as TV's "latest Dr. McDreamy" by the New York Times for this role.

In his return to theatre in 2008, he appeared as King Arthur in Lerner and Loewe's Camelot with the New York Philharmonic from May 7 to May 10, following the footsteps of veteran actors Richard Burton and Richard Harris.

The actor did not set foot in America until he was 37. In 1988, Byrne married actress Ellen Barkin by whom he has two children, Jack Daniel (born 1989) and Romy Marion (born 1992). The couple separated amicably in 1993 and divorced in 1999. Byrne is a fan of Chelsea FC and resides in Brooklyn, New York.

In November 2004, Byrne was appointed a UNICEF Ireland Ambassador.