Rea was born in Belfast, Northern Ireland. One of four children in a working-class Presbyterian but nationalist family, he attended Belfast High School and the Queen's University of Belfast, taking a degree in English.

Rea trained at the Abbey Theatre School in Dublin. In the late 1970s, he acted in the Focus Company in Dublin with Gabriel Byrne and Colm Meaney. During the broadcasting ban on Sinn Féin imposed by Margaret Thatcher's government, in order to cut the 'oxygen of publicity', it was interpreted that Sinn Féin members could not be heard making statements expressing the views of Sinn Féin, so Rea was one of many actors contacted to provide an actor's voice to get around that problem.

After appearing on the stage and in television and film for many years in Ireland and Britain, Rea came to international attention when he was nominated for the Academy Award for Best Actor for the film The Crying Game. He is a frequent collaborator with Irish film maker Neil Jordan.

Rea has long been associated with some of the most important writers in Ireland. His association with playwright Stewart Parker (1941-1988) for example, began when they were students together at the Queen's University of Belfast.

Rea helped establish the Field Day Theatre Company in 1980 with Tom Paulin, Brian Friel, Seamus Heaney, and Seamus Deane. In recognition for his contribution to theatre and performing arts, Rea was given honorary degrees from both the Queen's University of Belfast and the University of Ulster in 2004.