He taught Sacred Scripture at several universities, participated at the Second Vatican Council as a peritus and was made a Chaplain of His Holiness on 20 September 1978.

On 8 March 1986, Mejía was appointed as titular bishop of Apollonia and an official of the Curial Pontifical Council for Justice and Peace.

His episcopal consecration took place on 12 April 1986 and was performed by Cardinal Roger Etchegaray with Archbishop Eduardo Martínez Somalo and Bishop Antonio María Javierre Ortas as co-consecrators.

On 21 February 2001 Mejía was appointed as Cardinal-Deacon of San Girolamo della Carità by Pope John Paul II in the consistory.

[3] On 13 March 2013 Mejía suffered a heart attack on the same day his fellow Argentine Cardinal Jorge Mario Bergoglio was elected as Pope Francis, the 266th pontiff of the Catholic Church.