Authorities countered by saying their evidence was preserved in a lab, while the evidence used in private testing was very questionable.
Sharp said the family is also outraged that police secretly followed one of DeSalvo's relatives to collect DNA evidence from a discarded water bottle to use in their testing.
A nephew of Sullivan's who for years maintained that DeSalvo did not kill his aunt and even wrote a book on the case pointing to other possible suspects acknowledged the new findings point to the man he'd defended.
Casey Sherman said he accepted the new findings after concluding that the DNA evidence against DeSalvo appeared to be overwhelming.
"I only go where the evidence leads," he said, thanking police and praising them "for their incredible persistence."
Casey Sherman also expressed sympathy for the DeSalvo family, whom he had aligned with in the past in a shared belief that DeSalvo didn't kill his aunt.
That belief was based on DeSalvo's taped confession to Sullivan's killing, which Sherman said in 2000 was inconsistent with other evidence in the case.
The families of DeSalvo and Sullivan jointly sued the state for release of evidence while pursuing their own investigation. Sullivan's body was exhumed in 1999 for private DNA testing as part of the effort.
Attorney F. Lee Bailey, who helped to obtain the confession from DeSalvo, said Thursday's announcement will probably help put to rest speculation over the Boston Strangler's identity.
Bailey had been representing another inmate who informed the attorney that DeSalvo knew details of the crimes. Bailey went to police with the information, and he said DeSalvo, who was already in prison for other crimes, demonstrated he knew details only the killer would know.
Bailey would later represent DeSalvo.
"It was a very challenging case," said Bailey, who lives in Yarmouth, Maine. "My thought was if we can get through the legal thicket and get this guy examined by a team of the best specialists in the country, we might learn something about serial killers so we could spot them before others get killed."