Egan was born in Strabane, County Tyrone in Northern Ireland in 1952. He attended the Slade School of Fine Art and the British School in Rome on a scholarship from the Arts Council of Northern Ireland.
In 1986 he became a member of Aosdána. Felim Egan lives and works in Dublin. In 1981 he represented Ireland at the Xie Biennale de Paris and in 1985 at the San Paulo Bienal. In 1993 he won the prestigious UNESCO prize in Paris, and in 1995 the Premiere Prize at Cagnes-sur-Mer.
His work hangs in numerous public collections including the Stedelijk Museum, Amsterdam; the Irish Museum of Modern Art, Dublin; the Ulster Museum, Belfast; the Metropolitan Museum of Art, New York, and the collection of the European Parliament. Large-scale commissions include works for Dublin Castle and the National Gallery of Ireland.