Brizzi, 50, was jailed at the Old Bailey for a minimum of 24 years in December for the murder of 59-year-old Gordon Semple at his flat in south London.
He died at HMP Belmarsh, the high security jail in Woolwich, south east London.
Brizzi, who met his victim on gay dating app Grindr, reportedly took his own life.
Figures released last month showed that suicides, assaults and self-harm behind bars have all surged to record levels, with 354 deaths in prisons in England and Wales last year, including 119 which were apparently self-inflicted.
Self-harm incidents jumped by nearly a quarter, while there were more than 25,000 assaults in the 12 months to September - equivalent to nearly 70 attacks every day.
The figures triggered new calls for reform of the prison system amid claims that jails are dangerously over-crowded.
A Prison Service spokeswoman said in a statement: “HMP Belmarsh prisoner Stefano Brizzi died in custody on Sunday.
“As with all deaths in custody there will be an independent investigation by the Prisons and Probation Ombudsman.”
Brizzi was arrested after police called to his flat to investigate a foul stench discovered the gruesome scene.
During his trial, the Italian admitted he was inspired by his favourite TV series Breaking Bad as he tried to get away with the killing by dissolving his victim’s flesh in an acid bath.
But the crystal meth addicted former Morgan Stanley IT developer denied he had cooked and tried to eat parts of the body with chopsticks, saying he had no memory of it.
Brizzi was found guilty of murder and sentenced by Judge Nicholas Hilliard QC to life with a minimum of 24 years, with seven years concurrent for disposing of the body.
The court heard evidence from an odontologist settled the matter of whether Brizzi had in fact cannibalised part of his victim.
On examining a rib discarded in the kitchen bin, the expert found that a bite mark did in fact match the defendant’s lower teeth.