Maj Gen Nick Welch, 57, claimed to live in London rather than at Blandford Forum, Dorset, near their schools.
Welch, who left the military in 2018, was convicted of fraud by a panel of senior officers after a four-week trial at Bulford Military Court.
He is believed to be the most senior officer to be court-martialled since 1815.
The Continuity of Education Allowance (CEA) allows children to remain at the same schools to enable their serving parent to be accompanied by their spouse as they are posted to different locations.
However, it cannot be claimed if a soldier's spouse is away from the military home for more than 90 days per year, the court heard.
During the four-week trial, the prosecution said Welch applied for the allowance on the basis both he and his wife would not be living close to the children.
But it claimed his wife Charlotte actually spent most of her time at a cottage in Blandford Forum, close to the £37,000-a-year Clayesmore School and the £22,500-a-year Hanford School.
An investigation was launched after a neighbour told authorities about the family's absence from London.
Welch denied being dishonest and said his wife was living with him for the majority of the time.
His barrister, Sarah Jones QC, said the CEA system and the 90-day rule were a "mess" and not strictly enforced.
A character reference from the former Commander of Joint Forces Command, General Sir Richard Barrons, said Welch was of "unimpeachable integrity".
But prosecutor Sarah Clarke QC said he had attempted to manipulate the figures regarding his family's locations to cover up his dishonesty.
A Ministry of Defence spokeswoman said: "It has been proven in this case that the retired Major General Nicholas Welch OBE did commit fraud and therefore he will be sentenced accordingly."
He is due to be sentenced on Friday.
He knows nothing and thinks he knows everything. That points clearly to a political career.