Leanne Zaloumis reportedly entered the house in the posh area of Holland Park via a downstairs window and roamed the property before coming face-to-face with the music and reality show mogul, who was relaxing watching TV.
She was apprehended by members of Cowell's security team as police were called to investigate the crime, and is currently being held in custody on one count of aggravated burglary.
Confirming the news, a spokesman for Scotland Yard says: 'Police were called at approximately 2235 hours on Saturday, 24 March, to reports of a disturbance.
""Officers attended the address and found a woman had forced entry to the premises. She was arrested and taken to a west London police station where she remains. A 29-year-old woman was arrested on suspicion of burglary.""
The woman, who is not thought to have stolen anything from The X Factor judge's home, is due to appear before a judge at West London Magistrates' Court on Monday (26Mar12).
A source tells DailyMail.co.uk, ""It was a frightening experience. Simon's fine but shaken up - because he didn't expect something like that to happen.""