Cruel Robert Peters, 56, murdered his daughter Sophia in her bed at the family's £1million home in Wimbledon, South West London, last November, as the schoolgirl asked "what are you doing?".
The killing came just over a month after depressed and suicidal Peters was found not to be a risk by a child protection team.
It can now be revealed Peters throttled his second wife, Francine Peters, when they were married between 1994 and 2009.
No report of the attack was ever made to police or medical staff, with Ms Peters only telling police when they interviewed her while investigating the murder of Sophia.
Describing the claims, Mr Justice Andrew Edis said: "In her witness statement she describes a number of episodes of violence directed against her by her then husband.
"In particular there was one episode so she says when he grabbed her round the neck and strangled her."
The woman said she had tried to hide the strangle marks with a roll-neck jumper in hot weather.
The revelations come after the court was told the father had previously thought about killing his daughter but didn't act until November 3 last year, knowing it would be the last time they were alone together before she went back to her £5,000 a term boarding school.
The Old Bailey heard the businessman had been depressed, fearing financial ruin, and had wanted his family to be "spared the pain and upset when he became bankrupt".
Peters originally admitted manslaughter on the grounds of diminished responsibility but denied murder, claiming he heard voices at the time.
But with his wife Krittiya Promsat, who was not at home at the time of the murder, due to give evidence against him on the third day of his trial, Peters indicated he wished to change his plea.
Jim Sturman QC, for Peters, told the court: "I have had a conference with Mr Peters this morning and he has given me clear instructions that he wishes to change his plea and that he will, if re-arraigned, plead guilty to murder."
Mr Sturman said the new position would be "devastating news to his family" sitting in the public gallery.
The millionaire, who had previously told police he was "without emotion" after strangling his daughter, nodded as he admitted the charge.
Peters had previously described the sickening attack, telling police that Sophia had just woken up and asked "what are you doing?" as he put the cord around her neck, strangling her for 20 minutes on the morning of November 3.
He then called 999, telling the operator "there's a murder".
When Peters was asked "who's killed them?" he replied: "I have."
When officers arrived, he told them: "She's upstairs, I've strangled her.
"My daughter, she's upstairs in her bedroom."
The dad, who had recently moved back into the family home after cheating on his wife for two-and-a-half years, had previously told police he was worried he would lose custody of his daughter.
He had recently ended the affair, which started after he met a married Home Office official online.
His daughter was found wearing a nightie with a black fleece dressing gown cord wrapped around her neck.
Little Sophia had been rushed to hospital but died the next day.
But despite Peters' fears of bankruptcy, the court heard that preliminary financial enquiries did not suggest he was in debt and that there were no defaults on his accounts.
Prosecutor Mukul Chawla, QC, said: "He said that he just knew that eventually it would run out and he was powerless to control it."
In the months before the murder, Peters had researched the "treatment of child killers in prison" and "premeditated murder" online.
Detective Inspector Helen Rance from the Homicide and Major Crime Command, who led the investigation, said: "Sophia was an innocent seven-year-old girl, much loved by her mother, brother and friends. She was tragically murdered by the hands of her own father in the most frightening way.
"Sophia had her whole life ahead of her, which was taken away so cruelly in an act of pure selfishness. Robert Peters has shown no remorse for the murder, and initially maintained a defence of diminished responsibility. However, due to the strong evidence against him, he has changed his plea to guilty.
"This was a particularly traumatic case to deal with for all concerned, and I hope that this conviction brings a degree of closure to Sophia's family."
Peters was remanded in custody and is expected to be sentenced Monday April 30.
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