There were fears the remains of Scottish-born Brady would be scattered on Saddleworth Moor - where they buried four of their victims.
Brady's executor Robin Makin gave assurances there was 'no likelihood' of this happening, but the Chancellor of the High Court, Sir Geoffrey Vos, ruled in October the issue of disposal should be taken out of Mr Makin's hands.
The Moors murderer died at Ashworth High Security Hospital in Maghull, Merseyside, having been there since 1985.
Terry West, the brother of ten-year-old victim Lesley-Ann Downey, told the Daily Mirror that Brady's funeral was too ceremonious.
He said: "My little sister didn't get to choose how she was buried, so I can't see why that evil swine should have any say in what happens to him.
"If I had my way, I would just flush his ashes down the toilet."
Brady handed victim Keith Bennett's family one final insult from his deathbed - by refusing to reveal where he buried the 12-year-old.
The boy's mother, Winnie Johnson, died in 2012 after fighting tirelessly to find her son and provide a Christian burial.
It emerged shortly after Brady's death that police attempted to convince him to reveal the mystery location of the grave in his final hours.
Family lawyer John Ainley told Good Morning Britain: "The police spoke to me in the course of the evening, and they were trying to have access to his papers.
"That's difficult without consent from his solicitors and a court order. [The police] were trying, I think, to implore Brady at this very late stage to pass on any information or documents to them so they could carry out a meaningful search of the moors."
But Brady's lawyer, Robin Makin, said that if the killer did know where Keith's body was, he would have told police when they took him to the moor in 1986.
"He did go to the Moors a long time ago and I suspect that if there had been information for him that he could have provided, he would have provided it then," he told Radio 4's Today program.
He added: "I would very much hope that the remains can be found, but unfortunately I haven't got any information that's going to assist."
The sick killer was still claiming before his death that the horrific murders were entirely justified.
In disturbing letters, he even argued that governments and elites were allowed to kill people in warfare - and that he should be allowed to do the same.
"The question of global serial killers and thieves - politicians, bankers, military etc - forever unpunished and thriving is a separate question of legal/moral relativity, of course, constant throughout history," he wrote.
Hindley died in prison in 2002. Now Brady - who said repeatedly he wanted to commit suicide - has followed her to the grave.
An inquest into Brady's death heard he died of natural causes.
Home Office pathologist Dr Brian Rodgers said the cause of death was cor pulmonale, a form of heart failure, secondary to bronchopneumonia and chronic obstructive pulmonary disease, or lung disease.
The court heard Brady, who was a heavy smoker up until the smoking ban, had "very severely diseased" lungs.
In a statement, Tameside and Oldham councils said: "We are pleased that this matter is now concluded and we are grateful for the support and professionalism shown to ensure Ian Stewart-Brady's body and remains were disposed of expediently at sea in a manner compatible with the public interest and those of the victim's relatives."
The sadistic crimes of Ian Brady and Myra Hindley shocked the nation to its core. Across Britain there was an outpouring of loathing for the pair who snatched children off the street, sexually abused them and tortured them to death.
The evidence seen and heard at their Chester Assizes trial chilled the hearts of those who sat through it.
Their first victim was 16-year-old Pauline Reade, who vanished on July 12 1963, on her way to a disco near her home in Gorton, Manchester.
She was lured to the moors by Hindley who said she had lost her gloves there and needed help finding them.
It was two decades later when Pauline's grieving parents discovered exactly what had happened to her.
Her body was discovered in 1987 after the murderers confessed to the killing.
They were taken to bleak Saddleworth Moor where they located the shallow grave dug over 20 years before.
Pauline was still wearing her pink and gold party dress and blue coat.
Brady had beaten her about the head and cut her throat with such force that her spinal cord was severed.
Pathologists said it was impossible to say whether Brady had sexually assaulted her.
Four months after Pauline vanished, the day after President John F Kennedy's assassination in the US, 12-year-old John Kilbride became Brady's second victim.
In the shadow of the presidential assassination little attention was paid to the disappearance of the Manchester boy.
John was lured on to the moor where he was sexually assaulted and murdered. Brady took a photograph of Hindley standing on the edge of his grave holding her pet dog. The photograph would later lead police to the young boy's resting place.
The body of the third victim, Keith Bennett, 12, has never been found.
Keith died after leaving his home in Chorlton-on-Medlock in Manchester on June 16 1964.
Police mounted an intensive search of the moor in 1986 amid reports that the pair had confessed to his murder.
But even though Brady and Hindley were both permitted to travel to the moor to try to remember where the boy's remains were, they were not found.
Last moments recorded
It was Brady and Hindley's next killing that sealed their reputation for pure wickedness - the murder of 10-year-old Lesley Ann Downey on Boxing Day in 1964.
She became their youngest victim when she was lured from a fairground to the house Hindley shared with her grandmother in Hattersley.
Brady stripped, sexually abused and tortured her, forcing her to pose for pornographic photographs.
Her last moments were recorded on a harrowing 16-minute, 21-second audio tape.
The terrified girl begged for mercy, called out for her mother and appealed to God for help before her voice was stifled forever.
The tape was recorded at the house in Wardle Brook Avenue, Hattersley, as Lesley Ann pleaded with them "Please God, help me" and "Don't undress me, will you?"
Her cries reduced the judge, jury, courtroom spectators and even hardened police officers to tears.
John Stalker, former deputy chief constable of Greater Manchester, who was then a detective sergeant, expressed the feelings of many in the courtroom when he said: "Nothing in criminal behaviour before or since has penetrated my heart with quite the same paralysing intensity."
Detectives could not say exactly how Lesley Ann died. Her body was dug up naked except for shoes and socks.
Had the pair not made a crucial blunder in involving Hindley's brother-in-law David Smith in their next enterprise, the murder of Edward Evans, 17, might not have been their last.
Edward was lured from a gay bar to a home then shared by Hindley and Brady on the Hattersley estate at Hyde.
Smith was summoned to the house by a phone call on a false pretext.
He was then forced to watch as Brady attacked Evans with an axe, smothered him with a cushion and completed his grim task with an electrical cable.
• Pauline Reade, 16, was the couple's first victim. She was on her way to a local dance when Hindley persuaded her to get in her car. They drove Pauline to Saddleworth Moor where she was raped Pauline, beaten and stabbed. • John Kilbride, 12, was snatched from Ashton market on Saturday November 23, 1963. He was strangled and buried in a shallow grave. He was the second of Brady and Hindley's five victims. • Keith Bennett, 12, disappeared on the way to his grandmother's house. Hindley had lured him into her car and driven him to the Moors where he was murdered. The method of killing has never been made clear. The pair buried his body, which has never been found. • Lesley Ann Downey, 10, disappeared on Boxing Day. She had been snatched from the fair and taken back to Hindley's house. She was brutally assaulted with the ordeal captured on tape. •Edward Evans, 17, was the sick duo's final victim. He had just been to see Manchester United play when Brady lured in Edward. Brady repeatedly bludgeoned Evans with an axe