Donald Neilson, the serial killer known as the Black Panther, died on Sunday, the Ministry of Justice said.
The 75-year-old was taken to hospital from Norwich prison with breathing difficulties and was pronounced dead at 6.45pm, the Prison Service said.
"HMP Norwich prisoner Donald Neilson was taken to outside hospital in the early hours of Saturday 17 December with breathing difficulties," a spokesperson said.
"He was pronounced dead there at approximately 6.45pm on Sunday 18 December. As with all deaths in custody, the independent Prisons and Probation Ombudsman will conduct an investigation."
Neilson murdered three people between 1971 and 1974 in a string of sub-post office robberies.
His final victim was Lesley Whittle, who was a 17-year-old heiress from Shropshire.
He kidnapped her in 1975 and left a ransom demand for £50,000. Neilson killed her after a series of misfortunes resulted in the ransom failing to be delivered.
Whittle's body was found in an underground drainage system. She was hanging from the bottom of a ladder with wire around her neck.
Neilson was captured 11 months after Whittle's death, after which he was sentenced to life in prison.
The case was one of the most notorious murders of the 1970s.
Neilson committed about 400 burglaries without being caught before committing his first murder.
In February 1972 he broke into a sub-post office in Lancashire and shot and injured a postmaster, Leslie Richardson, who confronted him in the act. In 1974 he shot and killed Donald Skeeper in another sub-post office robbery in North Yorkshire. Seven months later he shot and killed post master Derek Astin in a similar robbery in Accrington.
The nickname 'Black Panther' was coined when Astin's wife said of the killer that he was "so quick, he was like a panther".
Neilson also shot Sidney Grayland in yet another post office heist in November 1974, and savagely beat his wife Margaret Grayland to avoid being recognised.
In 2008 Neilson applied to have his whole life term reduced to 30 years, but his appeal was rejected.
At the time Justice Teare said: "It is plain from the sentencing remarks of the judge that the applicant was ruthlessly prepared to shoot to kill if he considered such action necessary.
"The murder of the young girl in March 1975 followed upon an abduction of her for gain. The location and manner of her death indicates that she must have been subjected by the applicant to a dreadful and horrific ordeal."
In the same year it was revealed that Neilson was suffering from Motor Neurone Disease.