The settlement has been claimed as the first such payment by an education authority since schools were legally required to introduce anti-bullying policies in September.
The parents of John Carnell claimed that he had been the victim of persistent bullying at Harrogate Grammar School in north Yorkshire - and had sued the local education authority for compensation.
But the offer from North Yorkshire County Council, made on the understanding that the council does not accept liability, will now prevent the planned court appearance.
The boy, then aged 12, was said to have been physically and verbally bullied for a year, before his parents took him out of the school.
The family has since set up an anti-bullying internet site - Bullying Online - which offers advice and information to pupils who are being bullied and their parents.
Mixed feelings
Speaking on behalf of the family, a solicitor said that they considered the offer from the council as a "victory", but that they had mixed feelings about not being able to take their case to court.
"They wanted to go to court because they felt the school had not done enough to protect their son but they are delighted that John, who is now 18, will not have to relive what happened to him."
The school also does not accept that it has behaved negligently, saying that the settlement will spare further expense and disruption.
A statement from the school said: "North Yorkshire County Council has agreed to pay a sum of money into court, with no admission of liability, to save further expense and disruption to the grammar school over allegations which the school has always vigorously denied.
"This was done in an attempt to resolve the matter without the need for more litigation, which would only have had a damaging effect on the staff and education services."
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