The appointment was announced Wednesday in Washington by Archbishop Carlo Maria Vigano, apostolic nuncio to the United States.
Caggiano, 54, succeeds then-Bishop William Lori of Baltimore, who was named archbishop of Baltimore in March 2012.
Msgr. Jerald Doyle has been as administrator of the diocese since May 2012, and he will continue to serve in the post until Caggiano is installed.
No date has been announced for the installation.
"Most importantly, he is a man of deep faith, love for the church and commitment to the Gospel. On behalf of the clergy, religious and laity, we welcome him with open arms and with our prayers that God will bless him as the shepherd of our diocese," the priest said.