Hindley and Brady buried four of their victims on Saddleworth Moor, Greater Manchester.
During that visit, after being on the moors for just one hour, he "discovered the junction of streams" he remembered and wrote that he felt "relieved".
He said: "I do not want to comment on Brady at all. It's closure for our family".
"Whilst we are not actively searching Saddleworth Moor, we will act on credible and actionable information that will help lead us to him", he added.
His accomplice, Hindley died in prison in 2002 aged 60. Bennett's family continue their search to this day for his body.
The slaying of Brady and Hindley's youngest victim, Lesley Ann Downey, aged 10, at Christmastime in 1964 sealed their reputation for pure wickedness.
"We can confirm a 79-year-old patient in long-term care at Ashworth High Secure Hospital has died after becoming physically unwell".
Lord Pendry, former MP for Stalybridge and Hyde, said he believed Brady's "jealousy" of Hindley motivated the killer to agree to return to Saddleworth Moor in 1987 in an attempt to find Keith Bennett's burial place.
Solicitor John Ainley, who represented Mrs Johnson and works closely with Keith's brother, Alan, said he had written to Brady less than two months ago.
Terry Kilbride, the brother of John Kilbride, Brady and Hindley's second victim, told the Sun he would celebrate Brady's death.
His request was rejected after Ashworth medical experts said he had chronic mental illness and needed continued care in hospital.
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I've got five letters that Ian Brady sent to me over the last 15 years - and many of them were rants about his treatment at the hospital about how he wasn't being understood, about how he was too intellectual, too clever for those who were trying to read his complicated mind.
He campaigned for several years to be moved from Ashworth to a Scottish prison where he would not be force-fed and would be allowed to die if he wished.
Since 1999 Brady had been calling for his right to die.
When he was sentenced in 1966, the judge said he was wicked beyond belief. The thoughts of everyone within Greater Manchester Police are with the families who lost loved ones in the most painful and traumatic way.
"It is especially saddening for the family of Keith Bennett that his killers did not reveal to police the whereabouts of Keith's burial site".
Mr Makin, the executor of Brady's will, said he was called to go and see the murderer hours before his death at 6.03pm on Monday.
He said: "I don't think useful information is going to come from him".
The circumstances of twisted Brady's death were not suspicious, the inquest heard.
He also killed Pauline Reade, 16, and 12-year-old Keith Bennett.
In 2012 Brady's health advocate, Jackie Powell, was questioned by police after she told a television documentary Brady had given her a sealed envelope to pass to Mrs Johnson in the event of Brady's death.
Conceding that he did not have the legal power to withhold the body he said the decision was the "right and proper moral judgment to make" as it would be "offensive" if they were.