Cardinal László Paskai died at the age of 88, he had served in the role for fifteen years, from 1987 to 2002.
Vatican Radio has reported that he had suffered a long battle with cancer.
He was one of the Cardinal electors in the 2005 papal conclave that elected Pope Benedict XVI.
219 members remain in the College of Cardinals, 120 are still eligible to take part in a Papal election.
It reads: "I offer prayerful condolences to you, the clergy, men and women religious and lay faithful of the Archdiocese of Esztergom-Budapest, and I thank Almighty God for his many years of service to the Church in Hungary.
"In commending his soul to the merciful love of the Father and uniting myself spiritually to all assembled for the solemn funeral rites, I impart my apostolic blessing as a pledge of consolation and peace in the Lord."
