Sophie Sotello, 46, quit her job as an office manager 15 years ago to educate her children.
She was convicted last year for failing to comply with a school attendance order for her youngest son, Gabriel.
The case was bought by the Royal Borough of Kensington and Chelsea but Ms Sotello appealed the conviction and won her case at the Old Bailey.
All three of her children, including her 20-year-old son and 17-year-old daughter, were home-schooled but this case was about the education of her youngest.
Judge Richard Hone QC led the appeal panel and dismissed the original City of London Magistrates' Court conviction.
He directed that school attendance should stop.
Outside court, Ms Sotello said: "I knew right was on my side. My kids learned to quote Churchill - 'If you're going through hell, keep going'."
But the borough's lawyer, Sue Obeney, told the court the legal affair would not have been necessary had matters been addressed 18 months ago.
Ms Sotello had refused to "engage" with officers and made threats, such as saying her company would charge Â£5,000 for her to attend a meeting, said Ms Obeney.
Ms Sotello said she "had nothing against" the schools in Chelsea, but said: "It's simply that school is not the right fit for every child."
She said she had a "co-parenting agreement" with her husband, who works as a deputy director at Sotheby's, as they go through a divorce.
The former manager said she had also taken her oldest son, now 20, who she described as musically "gifted", out of school after he was "smacked on the wrist every time he touched the piano".
A mother-of-three has won a battle against a west London borough to school her 10-year-old son at home.