On October 18, 1927, Valeri was appointed Titular Archbishop of Ephesus and Apostolic Delegate to Egypt and Arabia. He received his episcopal consecration on the following October 28 from Donato Cardinal Sbarretti, with Archbishop Pietro Benedetti, MSC, and Bishop Giuseppe Angelucci serving as co-consecrators. Valeri was later named Nuncio to Romania on July 1, 1933, and to France on July 11, 1936. In August 1942, the nuncio disputed Marshal Pétain's claim that Pope Pius XII understood and approved of France's increased hostility towards the Jews . He was awarded the Grand Cross of the Légion d'honneur upon leaving France in 1944 to again work in the Secretariat of State, specifically the Congregation for Extraordinary Ecclesiastical Affairs. After becoming President of the Central Committee for the Holy Year on June 28, 1948, Valeri was made assessor of the Sacred Congregation for the Oriental Churches on September 1 of that same year.
He was created Cardinal Priest of S. Silvestro in Capite by Pius XII in the consistory of January 12, 1953. Pope Pius advanced him to Prefect of the Sacred Congregation for Religious five days later, on January 17. Valeri was one of the cardinal electors who participated in the 1958 papal conclave that selected Pope John XXIII, who had earlier succeeded him as the French nuncio. The Cardinal lived long enough to only attend the first session of the Second Vatican Council in 1962, and to participate in the conclave of 1963, which resulted in the election of Pope Paul VI.
Valeri died in Rome, at age 79. He is buried in his family's tomb in Santa Fiora.