Archbishop Anthony Apuron had been accused of molesting altar boys when he was a parish priest during the 1970s. The allegations by at least three former altar boys emerged in 2016.
The Holy See said Apuron had been found guilty of some of the accusations against him and would be removed from his post.
"The Apostolic Tribunal of the Congregation for the Doctrine of the Faith, composed of five judges, has issued its sentence of first instance, finding the accused guilty of certain of the accusations and imposing upon the accused the penalties of privation of office and prohibition of residence in the Archdiocese of Guam," the Vatican said in a statement.
The Holy See added that the sentence was subject to appeal and would be effective only in the absence of appeal.
A separate set of accusations have also been levelled against former priest Louis Brouillard, who was a cleric in Guam, a US island territory in the Western Pacific, in the 1950s.