Jennifer Kiely, 35, was found with a pushchair on top of her in a seafront shelter in Eastbourne, East Sussex, on 22 January 2005.
The attack was thought to be sexually motivated but no one was ever charged with her murder.
DNA recovered from a cigarette butt at the scene matched DNA on the victim’s body, but at the time, no match was found.
However, police now say the forensic evidence is “overwhelming” and have named Ms Kiely’s killer as Keith Dowbekin.
The 60-year-old died in 2014, aged 60, and was also known as Keith Black and Keith Broadbent.
Dowbekin had been associated with members of Eastbourne’s homeless community like Ms Kiely, said Sussex Police, and had been arrested over separate rape cases in Great Yarmouth in 2003 and 2004, before being released without charge.
His DNA was not taken, in line with Norfolk Police’s procedures at the time.
Detective Chief Inspector Simon Dunn said a breakthrough in DNA technology in 2018 allowed police to trace and identify multiple people who shared similar parts of the DNA found at the crime scene.
DNA from a man in the north of England last year was the “final piece of the puzzle” and led to Dowbekin officially being made a suspect.
It was only then that police learned of his prior arrests for rape.
DNA obtained from Norfolk Police in relation to those cases matched the Eastbourne murder scene.
Police also said the suspected killer had given DNA as a witness to a separate murder in 2003 – but crucially, it wasn’t added to the database as he wasn’t a suspect.
“In 2003 and 2004, there was no provision to take DNA from people who were arrested, DNA was only taken from those who were charged with an offence – that is different now,” said DCI Dunn.
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Jennifer’s family said they were “grateful for the resolution of her case and for the hard work of those who never gave up”.
They described her as “more than her struggles” – a “gentle, funny and creative soul who loved music and cared deeply for others”.
“While this brings a sense of closure, it does not erase the loss of a kind, loving and vibrant woman who meant so much to those who knew her, especially her children,” they added.
“I hope her story encourages compassion for those experiencing homelessness and the stigma surrounding mental health.”
