He served as prefect of the Vatican's Congregation for the Causes of Saints from his elevation to the cardinalate by Pope Paul VI in 1973 until his death two years later.
He attended the seminary in Acqui before being ordained to the priesthood by Bishop Lorenzo Del Ponte on 6 June 1936.
From 1938 to 1942, Raimondi was secretary of the Guatemalan nunciature, during which time he was raised to the rank of a Privy Chamberlain of His Holiness on 3 March 1939.
On 24 December 1953, Raimondi was appointed Titular Archbishop of Tarsus and Nuncio to Haiti,[1] and Apostolic Delegate to the British and French West Indies.
He received his episcopal consecration on 31 January 1954 from Cardinal Adeodato Giovanni Piazza, OCD, with Archbishop Antonio Samoré and Bishop Giuseppe Dell'Olmo serving as co-consecrators, in the church of San Carlo al Corso.