Brady in police custody prior to his court appearance for the Moors Murders.
Hindley died aged 60 in 2002.
Brady, 79, who now uses the name Ian Stewart-Brady, is a patient at Ashworth Hospital in Merseyside where he is reportedly receiving palliative care.
The murderer, who was 79 when he passed away, was confirmed to have died in prison by Mersey Care NHS Foundation Trust.
At a court hearing in February lawyers said he had been bedridden for the last couple of years and it was "fair to say" he is terminally ill, with emphysema among his ailments.
Brady and his wife Myra Hindley tortured and murdered five children in the Yorkshire Moors in the 1960s.They later confessed to two other murders.
A criminal and alcoholic before he was sent to prison Brady had been on several hunger strikes arguing he should be allowed to die.
Nearly 20 years later, in 1985, he admitted the murders of Pauline Reade, 16, and 12-year-old Keith Bennett.
In one of her pleas for parole, Hindley wrote, 'Within months he [Brady] had convinced me that there was no God at all: he could have told me that the earth was flat, the moon was made of green cheese and the sun rose in the west, I would have believed him, such was his power of persuasion'.
They later admitted the murders of Pauline Reade and Keith Bennett.
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Hindley received two life sentences, plus seven years as an accessory in the Kilbride murder. Their bodies were eventually buried on desolate Saddleworth Moor in northwestern England.
During their trial the pair showed no remorse for their victims and although Brady accepted that he would never be released Hindley tried to gain her freedom before her death.
Eventually caught and jailed for life in 1966, Brady refused to tell the Bennett family where their son was buried.
As before, Brady and Hindley took their victim to Saddleworth Moor on the pretext of searching for a lost glove.
Brady, who was born in Glasgow but later moved to Manchester, was jailed at Chester Assizes for the murders of 12-year-old John Kilbride, Lesley Ann Downey, aged 10, and Edward Evans, 17.
It was there that he met Hindley and it is said she fell completely under his influence.
They recorded her at their home in Wardle Brook Avenue, Hattersley and her cries reduced the judge, jury, spectators and even hardened police officers to tears.
Hindley lured him into the back of her van, where Brady was waiting, by asking him to help load some boxes.
The pair summoned Hindley's brother-in-law, David Smith, to the house on a false pretext and forced him to watch as Brady murdered Edward.