Graham Sate, 25, of Grimsby, was also convicted of cruelty towards Lauren Creed by a jury at Norwich Crown Court.
Lauren's mother, Sharon Creed, 25, a Senior Aircraftwoman in the RAF, also from Grimsby, had admitted two charges of cruelty towards her daughter at an earlier hearing.
Last night it emerged that Sate had been out of prison for only 10 months when he murdered Lauren at her home.
Minutes after finding him guilty of her murder, the jury was told that he had previously been convicted of the attempted murder of a taxi driver and of a vicious attack on a fellow inmate while in jail.
Sate, who was living with Lauren and her mother when the girl was killed, showed no emotion as details of his previous violence were disclosed.
Yesterday, Norfolk social services refused to discuss why Lauren had not been placed on its child protection register despite the presence in her household of such a violent person, and a series of complaints by concerned neighbours. The local authority said it would be inappropriate to comment ahead of the sentencing of the pair tomorrow.
Lauren was declared dead shortly after paramedics found her on the floor of her home at RAF Coltishall in October 1997, Norwich Crown Court was told during the five-day trial. Pathologists said she had died as a result of having her liver split and crushed against her spinal column. The court was told she had either been punched or kicked as she stood against a wall, or stamped on as she lay on the floor.
The court was told that Lauren, 3ft 1in and 4st 6lb, was found to have 167 fresh bruises and abrasions and a fractured rib. Doctors said the injuries had been inflicted during a "sustained attack" in the 24 hours before her death.
Sate had lived with Creed and Lauren for four months in married quarters and Lauren even began calling him "Daddy".
In court, Sate, who denied murder and cruelty, blamed Lauren's death on Creed and said he had done nothing more that occasionally smack the child's bottom. But a tape recording of the dead child's voice contradicted this, and the startling piece of evidence may well have secured the conviction of her murderer.
On the tape, made by next-door neighbour Sofiah Baker three months before Lauren died, the girl says: "Daddy punched me in the belly today, slapped me, punched me."
Mrs Baker had taken the matter into her own hands after her husband, Gregg, an RAF police corporal, pointed out swellings on Lauren's cheeks and jaw.
But Sate, whom they approached, said any bruises were caused by accidents. Norfolk social services apparently believed the explanation.