“All to no avail,” Rigoberto Reveron said via telephone from his home in Lorain, Ohio. “We didn’t know he had already been buried.”

In March 2010, Mr. Reveron filled out an electronic form concerning missing and unidentified people. Within a few days, he got a call from Ben Figura, the director of identification at the medical examiner’s office, who said, “I personally want to get involved and help you find him.”

The medical examiner’s office got critical biographical information about Mr. Reveron’s son: He was a high school and college wrestler who after college was found to be bipolar. He had an appendectomy, had donated a kidney to his older brother and had the scars from both operations.

That information, Mr. Reveron said, matched “a John Doe buried on Hart Island.” The match was then confirmed by DNA, using an autopsy sample and DNA taken from the parents.

“In April 6, 2010, our chief of police and pastor of our church came looking for my wife and I to tell us a positive match had been made,” Mr. Reveron said. “Six years later.”

The medical examiner’s office declined to discuss any case in which an identification had been made, citing privacy concerns. But the cases, according to a person familiar with the identification process, have also included Sean Wheeler, a professor at John Jay College of Criminal Justice who disappeared in late 2003 after a car accident on the Henry Hudson Parkway. His body was found about three months later, floating in the Hudson River by a ferry captain, but it was not until 2010 that a match was made.

Mr. Wheeler’s relatives said they had been in touch with the medical examiner’s office in early 2004, so it was somewhat frustrating to have had to wait so long for an affirmative match. The confirmation of Mr. Wheeler’s death “was very depressing,” an aunt, Kimberly Wheeler, of Independence, Mo., said. “It shouldn’t have taken so long if they’d put any effort into it.”