In a note, Prato wrote he had decided to take his own life because of the "lies" told about him and the "media hype" surrounding the case.
Prato was being detained in the jail in Velletri and a hearing in the trial against him was set to take place on Wednesday.
Prato and fellow suspect, Manuel Foffo, were accused of homicide aggravated by cruelty after they allegedly tortured, beat and stabbed Varani to death during a cocaine and alcohol-fuelled party on March 4, 2016.
"We just wanted to kill someone to see what effect it had on us," Foffo allegedly told prosecutor Francesco Scavo after being arrested.
Last year, a detention review court rejected Prato's appeal to be released from preventive custody.
Velletri prosecutors have opened an investigation into Prato’s death.
Justice Minister Andrea Orlando said on Tuesday that he had asked prison authorities for a "detailed report" on the suicide to check whether Italy's suicide prevention protocol had been respected.
Orlando said that he believed Prato was being watched closely by a psychologist and had not shown signs of instability.
The minister added that psychological help for prisoners had recently been boosted and the number of prison suicides had fallen.
With ANSA
