The priest was attached to an Archdiocese in the US before his death and owned 40 acres of farmland in Ireland, which he left to two of his cousins in a 2001 Irish will.
However, when he made a US will in 2017 for his American property, it included a revocation clause which did not mention the Irish land and was not intended to revoke the 2001 Irish will, the cousins argued.
The priest died in 2019, aged in his 70s, after suffering a heart attack.
The cousins brought a High Court application, with the American lawyer who drew up the US will as respondent, seeking to have the Irish will declared valid.
The court heard the priest made the Irish will in August 2001 and appointed three members of the cousins' family as executors. The cousins looked after the priest's land, and it was intended it would go to one of them and become part of his farm.
However, in April 2017, he made another will which contained the standard revocation clause of all previous wills and codicils, and in which he made arrangements for his American property after he died.
This included investments and a motor vehicle and his funeral arrangements.
The cousins, in their court application, said they had a very close relationship with the priest and often discussed farming matters with him.
The American lawyer who drew up the US will was not aware of the Irish property and had said the standard revocation clause inserted into that will was not intended to revoke the 2001 Irish will, they said.
The application was heard by Mr Justice David Nolan on Friday following submissions from Daniel Cronin SC, for the cousins. There was no appearance for the US lawyer.
The judge said he was satisfied to grant the order sought, and admitted the Irish will to probate.
The judge said, before his death, the priest had strong links with the defendants and discussed with them how his 40 acres were looked after.
The judge noted it was clear the priest and his cousins had a close relationship.
He added it was also clear from his American will that he was "a man of particularity", and if he had wanted his Irish estate to be included in the US will he would have said so.
The judge added that the priest also had discussions with one of his cousins about the land three months before he died.
His US attorney had also expressed surprise that there was any Irish land, the judge said.
He found it would be contrary to the priest's intentions if the court was to find the Irish will had been revoked, and he therefore declared it to be valid.