Eamonn was born in Delgany, County Wicklow. He turned professional in 1968 and played on the European Tour from 1972, winning four European Tour tournaments. His best years were 1975, when he came third on the Order of Merit, and 1976, when he improved to second. He finished in the top 20 on the Order of Merit nine times in total and made the top 100 as late as 1999, when he was 47. In 2002 he joined the European Seniors Tour. He was a member of the GB & Ireland/European Ryder Cup team on four occasions, including the victorious team of 1987.