Albert DeSalvo admitted to killing Mary Sullivan and 10 other women in the Boston area between 1962 and 1964 but later recanted. He was later killed in prison.
The DNA finding "leaves no doubt that Albert DeSalvo was responsible for the brutal murder of Mary Sullivan" and it was "most likely" that he also was the Boston Strangler, Massachusetts Attorney General Martha Coakley said.
Authorities said recently that new technology allowed them to test semen left at the crime scene of Sullivan's death using DNA from a living relative of DeSalvo's. That produced a match with DeSalvo that excluded 99.9 percent of suspects.
To confirm the match, investigators unearthed his remains a week ago and said Friday that the odds that the semen belonged to a male other than DeSalvo were 1 in 220 billion.
"It's a great day. This is now full justice for my aunt, Mary Sullivan," said her nephew, Casey Sherman.
A lawyer for DeSalvo's family has said even a perfect match wouldn't mean he killed Sullivan. She was 19 when she died in January 1964, a few days after she moved from Cape Cod to Boston.
Eleven Boston-area women between the ages of 19 and 85 were sexually assaulted and killed between 1962 and 1964, crimes that terrorized the region and grabbed national headlines.
Law enforcement officials disagree about whether the same person killed all the women whose deaths were connected to the Strangler.
Sherman had once joined with the DeSalvo family in believing that Albert DeSalvo wasn't his aunt's killer.
He said Friday that he thinks there will always be unanswered questions related to the Strangler case, but when it comes to his loved one's slaying, his family finally has a sense of closure.
"He's the killer of my aunt, which is all this has been about for me," Sherman said.
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