American College in Rome from 1955 until 1958 and served as the Rector Magnificus of the Pontifical Gregorian from 1958 until 1963. Pope Paul VI appointed him as the Titular Archbishop of Ceramus (with the rank pro hac vice of archbishop since it was a titular see and not a titular archbishopric) and as the Coadjutor Archbishop "sedis datus" for the Quito archdiocese in 1964. He received his episcopal consecration on 19 March 1964 in Rome from Cardinal Carlo Confalonieri. He succeeded to the metropolitan see of Quito on 23 June 1967 after serving as its coadjutor which meant that he had the right of succession in that role. He attended the final two sessions of the Second Vatican Council as a bishop from 1964 until 1965. He attended the 1967 gathering of bishops in Rome from 29 September to 29 October and also became the President of the Ecuadorian Episcopal Conference; he had two terms from 1969 to 1973 and then 1975 to 1984. He attended several other episcopal gatherings in Rome spanning the next decade. Vega was made the Cardinal-Priest of San Roberto Bellarmino on 28 April 1969 and received his title on 30 April from Paul VI. He participated in the first conclave in 1978 that elected Pope John Paul I and the following conclave that October that saw the election of Pope John Paul II. In his role as a cardinal he was a member of both the Congregation for Catholic Education and the Congregation for Institutes of Consecrated Life and Societies of Apostolic Life. In 1979 he attended the Third General Conference of the Latin American Episcopate in Puebla in Mexico and attended a gathering of the College of Cardinals from 5–9 November 1979. He lost the right to vote in conclaves after he turned 80 in 1983. He resigned from the pastoral governance of the archdiocese in 1985 as was a requirement of canon law. Vega also attended his last conference of the Latin American Episcopate in the Dominican Republic from 12 to 28 October 1992. He died in his old see on 3 June 1994 and is buried in the archdiocesan cathedral. Beatification process On 21 February 2013 a formal request for the beatification process was lodged to the Congregation for the Causes of Saints in Rome. The C.C.S. granted their formal approval to the cause on 10 December 2015 with the declaration