Bropho had been due to be sentenced in the District Court of Western Australia next week after pleading guilty to abusing a nine-year-old girl he lured back to his Doubleview home from a nearby park.
His lawyer Clint Hampson confirmed on Thursday he had been informed by Hakea prison authorities of his client's death.
WA's Department of Justice would not confirm reports Bropho, who had an intellectual disability, had been assaulted.
In a statement, the department said a 40-year-old Aboriginal man had been found unresponsive in his cell just after 8am on Thursday.
"Prison staff provided first aid and paramedics attended but the man was unable to be revived," a spokeswoman said.
"The circumstances surrounding the death will be subject to a police investigation.
"The prison is assisting the investigation and two units have been placed in lockdown to assist police.
"WA Police will provide a report to the state coroner."
A police spokesman said major crime detectives were attending the prison to establish the circumstances surrounding the death.
Three St John WA crews attended the facility, a spokeswoman said.
Bropho had been living under the supervision of an NDIS carer in July last year when he committed the sexual offences that led to his imprisonment.
Youth custodial officers have meanwhile walked off the job at the troubled Banksia Hill juvenile detention centre.
CPSU/CSA branch secretary Rikki Hendon said negotiations had broken down with the state government after almost a year of bargaining on a new pay deal.
Conditions at Banksia Hill have been described as dangerous with staff shortages contributing to repeated lockdowns.
A youth custodial officer last month suffered a suspected fractured skull after being hit by objects allegedly thrown by detainees who scaled fences and rooftops.
"It is time the government started treating its frontline workers at Banksia Hill with the respect they deserve and stop avoiding their responsibility to workplace health and safety," Ms Hendon said.
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