After serving eight-year sentences, they were granted lifelong anonymity that saw them released under new identities in 2001.
Following his arrest in November, the Attorney General launched an investigation into claims his identity had been revealed on social media.
In 2013, two men who posted images they claimed to be of Venables and Thompson were given nine-month sentences, suspended for 15 months.
Breaking the injunction on identifying them carries a punishment of up to two years in prison.
James's father Ralph Bulger has previously called for Venables to be stripped of his anonymity.
When news of his latest arrest emerged, James's mother Denise Fergus said: "Venables has now proved beyond any doubt what a vile, perverted psychopath he has always been."
Secret trials are extremely controversial as they run counter to the principle that for justice to be done it must be seen to be done.
The only other secret trial in recent memory was that of two men who were charged in 2014 with serious terrorism offences were kept anonymous and the press and public were excluded from their trial.
At the time MPs and civil rights campaigners said it was an "outrageous assault" on the principles of open justice and set a "very dangerous precedent".
It is the second time Venables has been recalled to prison over child abuse images.
In 2010, Venables was sent back to jail for two years after pleading guilty to charges of downloading and distributing child pornography.
In September 2008, he was arrested on suspicion of affray after a drunken brawl and was given a formal warning by the probation service for breaching the good behaviour terms of his licence.
Later the same year he was cautioned for possession of cocaine after he was found with a small amount of the class A drug.
The murder of James Bulger is regarded as one of the defining crimes of the late 20th century, with the CCTV images of the young toddler being led away from the New Strand Shopping Centre in Bootle by Venables and Thompson imprinted on the memory of those who followed the traumatic case.
James had a bump on his forehead and was crying, but most bystanders did not intervene
His mutilated body was found on a railway line two-and-a-half miles away in Walton, Liverpool, two days after his murder.
The killing sparked a widespread debate about the age of criminal responsibility and how the justice system should treat under age offenders.