Illegal immigrant Andrezej Kunowski was jailed in March 2004 after strangling 12-year-old Katerina Koneva, in 1997, in the Hammersmith area of London.
The Polish-born dry cleaner, who was questioned by detectives in connection with the then-unsolved murder of 13-year-old Milly Dowler, died aged 53 in high security Frankland Prison, in Durham city, last September.
Kunowski, who attacked at least 30 women and children in the UK and in his home country, was serving a whole life tariff which meant he would never have been freed.
An inquest jury at Chester-le-Street heard Kunowski, who died suddenly in his cell, had a long history of heart problems and had undergone a heart bypass. He had previously suffered a heart attack and was diabetic.
After hearing evidence from Home Office pathologist Dr Nigel Cooper yesterday, County Durham Coroner Andrew Tweddle directed the jury to return a verdict of death by natural causes.
Kunowski, who was living in Acton, West London, when he was jailed, came to Britain in 1996 after absconding from a Polish prison, where he had been convicted of 17 rapes.
He killed Katerina Koneva, who had arrived from Macedonia in 1995, after following her home from school. Katerina's father returned home to come face to face with the killer and chased him into the street. He only discovered what Kunowski had done afterwards.