In the battle over Archbishop Sheen, both sides considered dividing his remains but were unable to come to an agreement. It became an all-or-nothing affair.

Bishop Jenky told the court during the legal dispute that he had received a verbal promise in 2002 from Cardinal Edward Egan, then the New York archbishop, that the remains of Archbishop Sheen would be transferred to Peoria at the appropriate time if that diocese led the effort to prove that he was a saint, a difficult and time-consuming process.

But Cardinal Timothy M. Dolan, who became New York’s archbishop after Cardinal Egan’s retirement, maintained that he and his advisers could find no such evidence of a promise, and said that the body should remain where it was.

With no legal recourse left, the Archdiocese of New York said on Monday that it would no longer stand in the way of the body’s transfer. Its resistance, it said in a statement, had been rooted “in a solemn obligation to seek to uphold Archbishop Sheen’s last wishes.”

“In light of the court’s denial of further appeal, the Trustees of St. Patrick and the Archdiocese will work cooperatively with Mrs. Cunningham and the Diocese of Peoria to arrange for the respectful transfer of Archbishop Sheen’s mortal remains,” the statement said.

Msgr. James Kruse, the vicar general of the Peoria diocese, said he was delighted by the news that Archbishop Sheen, a particular figure of veneration for Midwestern Catholics, as well as evangelists, would be coming home.

“The bishop is absolutely overjoyed, and I am, too,” he said. “We have been receiving a tremendous outpouring of support and gratitude.”