Sate, who was earlier found guilty at Norwich Crown Court, has been told that he must serve at least 25 years.
Sentencing, the judge, Mr Justice Newman, described him as a dangerous man who “did not hesitate to resort to violence”.
Sate, 25, murdered Lauren Creed less than a year after he was released from prison two-thirds of the way through a seven-year sentence.
He was also convicted of a charge of child cruelty.
Lauren’s mother, RAF senior aircraftswoman Sharon Creed, 25, had earlier admitted two charges of cruelty.
She was jailed for five years.
In the weeks before the five-year-old’s death, the authorities failed to act on signals that she was at risk from Sate.
He eventually punched, kicked or stamped on her so hard that her liver split in two.
When a pathologist examined her after she died at her home at RAF Coltishall, Norfolk, in October last year, Lauren had 167 fresh bruises or abrasions on her body, the court heard.
The jury heard that there were warning signs in the months leading up to Lauren’s death.
A neighbour, Sofiah Baker, became so concerned about the girl’s battered state that she taped her saying: “Daddy punched me in the belly today. Slapped me. Punched me.”
But the authorities failed to appreciate the seriousness of the youngster’s plight – and there were indications that serious errors were made by the police, the RAF police and by social workers.
The BBC’s Social Affairs Correspondent Niall Dixon says new guidance will now be issued to agencies in the wake of this case.
Lauren’s murder was not Sate’s first offence. He was jailed for seven years in 1993 after stabbing a woman taxi driver in Grimsby, then given a further 15-month sentence in 1995 for causing grievous bodily harm by throwing scalding water on another prisoner.
Detective Inspector Malcolm Chambers, who led the investigation into Lauren’s death, said Sate was “contemptible”.
“He is just a very cold, dangerous person clearly prone to extreme bouts of violence,” said Mr Chambers.
He said he had never seen injuries like the ones Lauren had suffered during his long career in the police.
Sate moved in with Creed a few months after leaving prison on Christmas Eve 1996.
When on leave from his ship he looked after Lauren during the day while Creed was at her job in the stores at RAF Coltishall.
In early July 1997 civilian and RAF police were called to a domestic dispute at the couple’s home.
It was then that Mrs Baker and her husband became concerned about Lauren’s bruised appearance and the tape recording was made.
At that stage Sate was still on licence to the probation service and could have been returned to prison.
But neither the police nor the RAF police informed Sate’s probation officer of the incident or about Lauren’s complaints.
Social services were informed but a social worker did not question Creed until early September.
Mrs Baker said the police did not take the tape from her until after Lauren’s death. The court was told that officers had regarded the 7 July incident as nothing more than a domestic matter.