The boy, who has emotional and behavioural difficulties and was living in care, was effectively, but not officially, excluded from a mainstream school in Devon in November 2001, when he was 13.
But Devon county council did not provide suitable alternative full-time education until September 2003 which "severely compromised" preparation for his GCSEs, Jerry White, the local government ombudsman said.
After investigating the boy's complaint, Mr White this week found that Devon had been guilty of "maladministration causing injustice".
The council has agreed to make pound;3,000 available for his education and to give him pound;250 in compensation.
The boy, who has not been named, said: "Before I lost my education I was told that I was so good at maths I could take my GCSE a year early but I am now having extra tutorials to catch up to the level I should be for my age.
"Devon education department wasted my time and could seriously have damaged my life.
"While I was not allowed to go to school I got involved in drugs, drinking and crime. I was arrested and nearly went to prison, but all the time I wanted to be in school."
At the time of the complaint the boy was in the care of Wokingham district council which placed him in a residential home in Devon.
His Devon school sent him to a full-time educational support service because of his behaviour, but when he was later asked to leave there for similar reasons, the school refused to have him back.
The school provided sporadic work for him to do at home for the next five months.
During the subsequent 11 months he had six hours of home tuition and two half-day outdoor pursuits sessions, followed by two months with an extra four hours of home education.
The boy was then given two months full-time at an educational project with minimal academic work, before being placed full-time in a pupil referral unit.
A spokesman for Devon said that since school governors had never officially excluded the boy, ordinary procedures had not applied.
He added that all the procedures referred to by the ombudsman were being fully reviewed.
friday forum: 10-part behaviour series. This week, swearing