Concurrently he studied at the Pontifical Lateran University, Rome, where he obtained a licentiate in theology; and later, a doctorate in utroque iure, both canon law and civil law; and at the Rome State University, where he earned a doctorate in letters.

In August 1959 he was nominated spiritual director of the Pontifical Roman Seminary and was member of the commission for the first diocesan synod of Rome.

He participated in the general congregations of Vatican II on the themes of ecumenism and religious liberty.

On 8 February 1975 he was transferred to the titular see of Monterano, with personal title of archbishop, and appointed vicegerent of the Diocese of Rome.

Canestri was made a Cardinal-Priest of Sant'Andrea della Valle by Pope John Paul II in the consistory of 28 June 1988.