O'Driscoll was born in Dublin to Frank and Geraldine O'Driscoll, both physicians. O'Driscoll's family was steeped in rugby. His father, Frank, played two games for Ireland and a cousin of his father, Barry, won four caps. However it was another cousin of Frank's, Barry's brother John, who really put the O'Driscoll name on the map: he represented Ireland 26 times and was a member of the Lions side that toured 1980 British Lions tour to South Africa and 1983 British Lions tour to New Zealand.