He served from 1953 to 1971 successively in the diocese of Anglona-Tursi as pastor; director of the center for social studies; diocesan assistant of the Catholic Action; professor of religion; vicar general.

The following year Pope John Paul II created him Cardinal-Priest of San Gioacchino ai Prati di Castello.

In 2000 Giordamo stood trial in Naples on charges of allegedly using Church funds to support his brother's loan shark operation.

Cardinal Giordano was admitted to the Monaldi Hospital in Naples with respiratory problems and died a week later on 2 December 2010, at age 80.

In the papal telegram of condolence sent on 3 December 2010 to Cardinal Sepe, Pope Benedict XVI offered prayers for the repose of his soul and the Apostolic Blessing to all those in mourning, stating that he learned of the prelate's death "with great sadness."