The duration and intensity of the children's daily physical activity levels were measured for periods of between three and seven days, when they were aged 11, using a device called an accelerometer, worn on an elasticated belt.
The accelerometer showed that the average daily number of minutes of moderate to vigorous exercise the 11 year olds clocked up was 29 for boys and 18 for girls.
The children's academic performance in English, maths, and science was then assessed at the ages of 11, 13 and 15 or 16.
The analysis showed that better results across all three subjects was linked to the amount of moderate to vigorous physical activity undertaken at the age of 11.
By the age of 15/16 exam results showed an increase in performance for every additional 17 minutes per day boys did and 12 minutes per day that girl spent doing intensive exercise at the age of 11.
The performance of girls in science subjects was particularly high among those who exercised regularly at 11, the report found.
More top news
Even colder tomorrow with clear sky and sunshine
A British couple who dropped an engagement ring down a grate have been reunited with the item and the officers who recovered it.
Cardinal Vincent Nichols, Archbishop of Westminster, was giving evidence to the independent inquiry into child sex abuse.