Bernardin's accuser withdrew his allegations the next year, saying the memories that occurred under hypnosis were "unreliable."
Cardinal Timothy Dolan of New York investigated the allegation against McCarrick, engaging the review board of the Archdiocese of New York, according to a statement from the Archdiocese of Washington.
In his statement, McCarrick said he was "shocked" by the allegations and had cooperated fully with investigators.
"My sadness was deepened when I was informed that the allegations had been determined credible and substantiated," he said. "I am sorry for the pain the person who brought the charges has gone through, as well as for the scandal such charges cause our people."
Susan Gibbs, who served as McCarrick's spokeswoman in Washington, noted that McCarrick "helped create the child protection policy in the United States and he's followed them. I am praying for everyone who is impacted by this news and by the situation."
Joseph Zwilling, a spokesman for the Archdiocese of New York, said that the allegation against McCarrick came to light in 2017 through the Independent Reconciliation and Compensation Programme, which was set up by the archdiocese to offer healing and compensation for victims of abuse in the church.
McCarrick was ordained a priest in 1958 and worked at Catholic University and then in Puerto Rico, before serving as a priest in New York from 1969 to 1981, when he became the first bishop of Metuchen, New Jersey. He rose to Archbishop of Newark before his appointment in Washington.