The 33-year-old Dutch engineer was found guilty at Bristol Crown Court of murder after strangling Yeates, 25.
After his conviction, it was revealed that he was obsessed with images of women being choked during sex and liked prostitutes and violent porn.
Avon and Somerset Police have now revealed that he was storing 30 images of young children being sexually abused.
As Tabak is already serving a life sentence, the Crown Prosecution Service will take no action over the findings.
An anonymous officer involved in the investigation said: “Tabak had 30 images depicting child pornography on his laptop computer at home.
They were all category four images.” There are five levels of seriousness for indecent photographs of children.
Category four images depict penetrative sexual activity with a child or children or children and adults.
Jurors in Tabak’s trial weren’t told that videos found on his computers had stark parallels with Yeates’ death, showing blonde women being choked during sex or bundled into car boots.
He also paid a prostitute for sex during a business trip to Los Angeles, two weeks before he murdered Yeates, on December 17 last year.
A judge said the information was “not relevant” to the trial.
Despite not knowing about his subversive sex life the jury still found him guilty of murdering Yeates, who lived next door to him, by a 10-2 majority.
Solicitor Nick Freeman has spoken out today, arguing that courts should hear if anyone accused of a crime is known to watch internet porn.
Freeman said in his Manchester Evening News column: “In my view, anyone watching internet porn should know that if they subsequently become a defendant or witness in criminal proceedings, their cyber spectating could be open to questioning in court, if relevant to the charge.”
Tabak was told that he would serve a minimum of 20 years before he could apply for parole.