A ruling by the European Commission for Human Rights in Strasbourg, to be made public next week, will allow Robert Thompson and Jon Venables - now both 17 - leave to appeal against their convictions.
The case will then be considered by the European Court of Human Rights, the highest court in Europe.
If judges rule the boys' human rights have been breached they could move that the whole trial was unlawful.
Although the UK government has powers to derogate rulings of the court, it would find it difficult not to accept such a ruling, which would mean that the law would have to change in regard to juveniles being tried in adult courts.
The two boys' solicitors have always argued that their trial was "degrading and inhumane" because it was held in an adult court.
They also claimed the 15-year sentences imposed on Thompson and Venables by the then home secretary, Michael Howard, were illegal. The law lords ruled in June 1997 that Mr Howard acted unlawfully.
A detailed report on the case, which will be published on Monday, will be considered by a 19-strong panel of judges. It may be two or three years before a decision is made.
The Home Office also suggested that the commission leaked its decision to the media before James Bulger's family had been informed.
In a statement, the Home Office said: "We understand that this morning the secretariat of the European Commission of Human Rights responded to press queries on the case of Thompson and Venables.
"The secretariat confirmed that the case had been referred to the court and that the findings of the commission would be published on March 15.
"We deplore the fact that this information was made available before the family of their victim could be informed. Arrangements had been made to do this in confidence on March 15 before the commission's findings were to be published."
The statement added that the referral of the case to the European Court of Human Rights was "merely the next stage in the process. "It does not mean that Thompson and Venables must be released."
James was two years old when he was abducted from the Strand Shopping Centre in Bootle, Merseyside, on 12 February 1993. His body was discovered two days later on a railway line in nearby Walton. He had been repeatedly beaten.
Thompson and Venables, who were just 10 years old at the time, were arrested days later. They were convicted of James's murder after a three-week trial at Preston Crown Court in November 1993. Both boys have been detained at secure accommodation ever since.
Thompson's solicitor, Dominic Lloyd, said yesterday he was unable to comment on the case until Monday. No one was available for comment from Venables' defence team.
At her home in Kirkby, Merseyside, James Bulger's mother, Denise Fergus, criticised the decision to allow the boys' legal challenge.
Mrs Fergus, 31, who has two children - Michael, four, and Thomas, aged one - married Stuart Fergus last September, after divorcing James's father Ralph Bulger. She said: "No one should forget the vile and monstrous crimes these two committed when they abducted James and killed him. They murdered him in the most horrific and despicable way imaginable, and they cannot deny that.
"Nothing can bring James back and nothing can wipe out what they did. To say they were degraded, or that their trial was inhumane, is ridiculous.
"All this legal wrangling is sickening. They are trying to get off on technicalities and it is time the British legal system and the Government stood up to Europe on this."
Rex Makin, Ralph Bulger's lawyer, said: "Every time there is movement in this case it is a reactivation of the wound and the grief that Ralph suffers from the loss of his child."