North Lincolnshire Council had challenged a judge's ruling earlier this year that it was liable to compensate Ryan Lewis Jenney for the head injuries which have left him seriously handicapped.
But Lord Justice Henry, sitting in the appeal court with Lord Justice May and Lord Justice Chadwick, dismissed the council's appeal, saying the court would give its reasons later.
Ryan, from Brigg, sustained major head injuries when, in November 1996, he was hit by a passing vehicle in Wrawby Road, Brigg - 1,000 metres away from Brigg Primary School where he was a pupil.
The appeal court's decision to uphold the judge's ruling opens the way for Ryan to claim six-figure damages from the council.
If settlement terms are not agreed in the meantime, the exact amount of his compensation will have to be assessed at another court hearing.
The appeal court heard Ryan suffered 'educational and developmental impairment' before the accident and was being educated in the school's special needs unit.
On the day of the accident, he had twice strayed outside school grounds, and it was on the second occasion that disaster struck.
The council's barrister, Robert F Owen QC, argued in the court Mr Justice Gray's decision had been against the weight of the evidence.
He described Brigg Primary as a 'well-disciplined and well-run school' and said there was nothing 'haphazard of defective' about perimeter security.
The council had 'applied its mind' to the security issue and staff at the school had been given full instructions, he added.
The judges announced the council's appeal would be dismissed. No date was given for when they will give reasons for their decision.