The 72-year-old former civil servant from Aberdeenshire is believed to have died from natural causes.
He was convicted of the murders in 1983 and was imprisoned at HMP Full Sutton maximum security prison in Yorkshire.
Nilsen died in prison on Saturday, 34 years into his life sentence, according to the Ministry of Justice.
He was named the Muswell Hill Murderer because a number of his murders were committed at his home in Muswell Hill in north London.
He is known to have attempted to kill seven other men and boys. He initially confessed in 1983 to having killed 15 victims.
The majority of his victims were vulnerable boys or men, many of whom were homeless or homosexual.
After luring his victims to their death, Nilsen would often sit with their corpses for days before dismembering them.
His crimes were only detected by chance – when a drain outside his home became blocked by the human remains he had tried to flush away.
He was jailed for life with a recommendation he serve a minimum of 25 years, on six counts of murder and two of attempted murder.
A Prison Service spokesman said: “Dennis Andrew Nilsen, date of birth November 23 1945, died in custody at HMP Full Sutton on Saturday, May 12 2018.
More from UK
Stage invader grabs mic during UK Eurovision performance
Royal wedding: Palace reveals document used by Queen to give consent
Poundworld future in doubt as owner plots discount chain sale
Troops join search for kidnapped Britons in Democratic Republic of Congo
Senior US bishop to give address at royal wedding of Prince Harry and Meghan Markle
WH Smith ‘sorry’ as tubes of toothpaste sold for £7.99 at hospital stores
“As with all deaths in custody, there will be an independent investigation by the Prisons and Probation Ombudsman.”