The jury reached the verdict against 81-year-old Arthur Perrault on Wednesday following a trial in Santa Fe in which several men testified that they had been abused by him as children.
The person involved in the charges said Perrault had touched him inappropriately as many as 100 times.
Authorities believe Perrault had numerous victims in New Mexico. However, the federal charges against him stemmed only from the treatment of one boy at Santa Fe National Cemetery and Kirtland Air Force Base in Albuquerque, where Perrault had been a chaplain.
Authorities said the federal charges of aggravated sexual abuse and abusive sexual contact carry no statute of limitations and the two sites are within federal jurisdiction.
Perrault's case marks a rare federal criminal prosecution of a former Catholic priest in the state where dozens of clergy abuse victims have won more than USD 50 million in settlements from the Santa Fe Archdiocese, which has filed for bankruptcy protection as a result of lawsuits.
Federal authorities said their decades-long pursuit of Perrault showed how far they were willing to go to hold him accountable.
Perrault maintained in court proceedings that he was innocent of the charges.
Church officials in Connecticut sent Perrault to a retreat in the secluded mountain town of Jemez Springs north of Albuquerque in the 1060s after he was accused of inappropriately touching young males. The facility was operated by the religious order Servants of the Paraclete.
The FBI returned Perrault to the United States to face charges in September after he was arrested in Morocco a year earlier on an Interpol warrant. Before his arrest, Perrault had been teaching for a decade at an English language school for children, authorities said.
He expressed surprise and disappointment that the US government continued to pursue him for decades-old transgressions, she said.
Perrault's attorney questioned the truthfulness of his victim and highlighted for jurors that his accusations against Perrault came in 2014 when media reports of abuse allegations against the former priest emerged.
At trial, Perrault entered and exited the court room with the aid of a walker, and he used a hearing aid to listen to his accusers' testimony.
He could face a maximum penalty of life in prison on the charge of aggravated sexual abuse. The charge of abusive sexual contact carries a maximum of 10 years in prison.
A sentencing hearing has not yet been scheduled.
In 2016, the Santa Fe Archdiocese published a list of 74 clergy members, including Perrault, who had been credibly accused of sexually abusing children in New Mexico.
The list was made public after decades of pressure from victims and their family members.
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