The 76-year-old was told last year that his appeal to be sent to a Scottish prison to serve his sentence was to be refused, but yesterday Judge Robert Atherton gave the reasons for the decision in a detailed ruling running to more than 100 pages.
Brady was told last June that he is to remain a patient at maximum- security Ashworth Hospital on Merseyside after a week-long mental health tribunal hearing.
The child-killer's £250,000 taxpayer-funded legal bid to be transferred to a jail was the first time he had been seen in public for decades and was criticised by victims' families as a "circus" and a "complete waste of taxpayers' money".
Glasgow-born Brady, who murdered five children in the 1960s with his lover Myra Hindley, was jailed for life in 1966.
The decision to reject his appeal was given by Judge Atherton, who chaired the three-man tribunal panel at Ashworth.
At the end of the hearing, the panel said Brady should remain in Ashworth on the grounds that he is insane and hospital staff are best placed to treat his psychosis.
Judge Atherton said in his full ruling: "The tribunal concluded that it has been demonstrated by this evidence that it is necessary in the interests of his own health and safety that he be detained in hospital for treatment and that appropriate treatment is available.