Colin Gregg, 75, from Gosforth, Newcastle, had denied indecently assaulting four boys while working as a teacher, beginning in 1963.
A jury at Leeds Crown Court found him guilty after a trial lasting almost a month. He was told jail was inevitable.
He had been accused of nine counts of indecent assault on boys aged between 10 and 14.
Gregg, the son of the founder of the Greggs bakery chain, was released on bail and will be sentenced on 30 March.
The court heard he abused one child in a swimming pool and others in a gym at his home.
'Position of trust'
He claimed to be the victim of a "police witch hunt" and had previously been found not guilty of a similar offence in 1997.
Gregg showed no reaction as he stood in the dock and heard the verdicts, which were returned after almost 12 hours of jury deliberations.
The jury was told how he used to be head teacher at The King's School Junior School, in Tynemouth, and also taught at Durham School.
He also worked as a social worker in Newcastle.
Judge Robin Mairs told Gregg the fact he was granting bail was no indication of sentence.
He said: "These are serious matters and a custodial sentence is inevitable."
John Dilworth, from the Crown Prosecution Service, said: "Throughout his life, Colin Gregg has been a successful businessman, respected teacher and committed charity worker.
"Those achievements have won him the gratitude of the community but, beneath his respectable veneer, he was sexually abusing young boys with alarming regularity.
"Colin Gregg exploited his position in society to abuse young boys, using them for his own sexual gratification. "
The trial at Leeds was a retrial, after a jury in Newcastle failed to reach a verdict last year.
Northumbria Police said Gregg was "in a position of trust which he used to sexually exploit children".
A spokesman for children's charity the NSPCC said: "Gregg shamelessly betrayed the trust vulnerable young children placed in him and his sickening campaign of abuse will have had life-long effects on his victims.
"It is thanks to their bravery in speaking out that he's finally been brought to justice.
"Gregg probably thought he got away with these crimes but this case is proof that victims of abuse will be listened to, no matter how much time has passed."
The heir to the Greggs bakery chain has been convicted of a string of sex offences against boys.