He took possession of the apostolic delegation on 4 October 1896.
He became an official of the Apostolic Delegation in 1919.
He was then counselor of the apostolic delegation to United States from 1947 to 1950.
From 1936 to 1940, he was secretary of the Apostolic Delegation to Japan.
In 1934, he was made Secretary of the Apostolic Delegation to Japan.
He was counselor in apostolic delegation in the United States in 1968.
The Holy See previously had an apostolic delegation, based in Bangkok, for the country.
In the 19th century was established Apostolic Delegation in Colombia.
Dell'Acqua was secretary of the apostolic delegation to Turkey and Greece from 1931 to 1935.
He was appointed as internuncio to Chile when the apostolic delegation was elevated to that rank in 1908.