Cardinal Erdö was born in Budapest on 25 June 1952. He studied in Esztergom, Budapest and in Rome (Pontifical Lateran University) gaining doctorates in theology and canon law.
He was ordained for the archdiocese of Esztergom on 18 June 1975 and taught in Esztergom, Budapest and at the Pontifical Gregorian University. He became Rector of the Peter Pazmamany Catholic University in Budapest in 1998.
He was appointed auxiliary Bishop of Szekesfekhervar on 5 November 1999 (titular bishop of Puppi) and consecrated in Rome on 6 January 2000 by Pope John Paul II. He became Archbishop of Esztergom-Budapest on 7 December 2002, becoming Primate.
Pope John Paul II made him a Cardinal at the consistory of 21 October 2003, with the title of Santa Balbina.