Bishop Caggiano was born in the Gravesend section of Brooklyn, New York, to Arnaldo and Gennarina Caggiano. His parents were Italian immigrants who came to the United States from the town of Caggiano, in the province of Salerno, in 1958. The younger of two children, he has a sister, Antoniette.
He attended Ss. Simon and Jude Elementary School in Gravesend and graduated from Regis High School in Manhattan in 1977. He then entered Yale University as a political science major, but later decided to enter the priesthood. In 1978, he entered Cathedral College in Douglaston, from where Caggiano obtained a Bachelor's degree in Philosophy summa cum laude in 1981.
After working as a sales representative for the Gregg division of McGraw Hill Publishing Company for 18 months, he studied at Immaculate Conception Seminary in Huntington, earning a Master's degree in Divinity.