He was appointed archbishop by the Emperor Henry III in consultation with the people of the archdiocese.
In 1048, he travelled to Rome with the Bishop of Toul to attend his confirmation as Pope Leo IX and to himself be consecrated Archchancellor of Gaul.
In 1049, he traveled to Rheims and Mainz to help promote ecclesiastical reform in the Lotharingian church.
In 1056, he joined Anno II, Archbishop of Cologne, Godfrey III, Duke of Lower Lorraine, and Henry I, Count Palatine of Lotharingia, in supporting the empress Agnes of Poitou during her regency.
Around 1060, Eberhard became embroiled in a war with Conrad I of Luxembourg that led to the intervention of Pope Nicholas II.