Lord Justice Munby said the father's religious beliefs could not prevail over the right of his children to be educated to the point where they could decide on their own futures.
Both parents are part of the Haredi community, the most conservative form of orthodox Judaism, in north London, but the mother wants the children to go to orthodox, not ultra-orthodox, schools. She said it would give them "infinitely superior opportunities".
Giving reasons for rejecting the father's appeal, Lord Justice Munby, sitting with Lord Justice Maurice Kay and Sir Stephen Sedley at the Civil Court of Appeal, said the dispute came down to whether the mother's views on education should prevail over the father's arguments based on his way of life.
He said the historic view that fathers had a "sacred right" over a child's education and upbringing did not reflect the modern world. He acknowledged that the education issue was of "transcendental importance" to the Haredi community but said it was a fundamental value of modern English society that every child should have equality of opportunity.
Lord Justice Munby added that it was society's objective to ensure that every child grows into adulthood equipped to decide what kind of life they want to lead.
Acting as a "judicial parent", the courts had to be "cautious about approving a regime which may have the effect of foreclosing or unduly limiting the child's ability to make such decisions in future".
The court upheld a previous decision that the children's welfare would be best served by their mother's proposals for their education.
During their 10-year marriage, the couple, in their 30s, and their children observed a strictly kosher regime and would not even switch on a light, catch a bus or make a telephone call on the Sabbath.
However, after studying at the Open University and forging a professional career, the mother said she was determined that her children, the youngest aged three, should have the schooling she never had.
The couple separated two years ago and the mother claims she has been ostracised by the Haredi community.
Her ex-husband accepted that, if he had his way, his eldest son would probably have no qualifications outside Judaism instruction beyond GCSEs, but his counsel, Eleanor Platt QC, told the court that he was deeply concerned that his ex-wife would lead his children away from the ultra-orthodox community into which they were born and denigrate his lifestyle in their eyes.
He particularly objected to the prospect of his daughters being sent to a mixed-gender school and to his children having unrestricted access to television, cinema, "certain newspapers", the internet and social networking sites.
The children were thriving at their current schools and moving them away from the lifestyle they had known all their lives would split them from their friends, who would be forbidden from associating with them, and cause them incalculable emotional harm, said Ms Platt.
The mother said she had every intention of bringing her children up within the orthodox Jewish tradition.
