Non-shared environmental influences, unique to each individual, accounted for the remaining differences.
Study leader Nicholas Shakeshaft, from the Institute of Psychiatry at King's College London, said: "Children differ in how easily they learn at school.
"Our research shows that differences in students' educational achievement owe more to nature than nurture.
"Since we are studying whole populations, this does not mean that genetics explains 60 per cent of an individual's performance, but rather that genetics explains 60 per cent of the differences between individuals, in the population as it exists at the moment.
"This means that heritability is not fixed - if environmental influences change, then the influence of genetics on educational achievement may change too."
Non-identical twins may grow up in the same environment, attending the same school and growing up in the same family in the same neighbourhood, but only half their genes are the same.
Identical twins, on the other hand, share both the same environment and all their genes.
Because of this, comparing the two sets of twins can help disentangle the effects of nature and nurture on exam grades.
If identical twins' scores are more alike than those of non-identical twins, it can be assumed that genetics plays a bigger role than the environment.
The scientists found that inherited genes were responsible for 58 per cent of the variability seen in results for the three compulsory core subjects.
Taking each subject separately, they accounted for 52 per cent of the grade differences for English, 55 per cent for mathematics, and 58 per cent for science.
Generally, genetics appeared to have a bigger influence on results for science subjects than for humanities, such as media studies, art or music - 58 per cent compared with 42 per cent.
The findings appear in the latest issue of the online journal Public Library of Science ONE.
Professor Robert Plomin, director of the Twin Early Development Study (Teds), also from the Institute of Psychiatry, said: "It's important to recognise the major role that genetics plays in children's educational achievement.
"It means that educational systems which are sensitive to children's individual abilities and needs, which are derived in part from their genetic predispositions, might improve educational achievement."
Professor Michael O'Donovan, from the Medical Research Council (MRC), which funded the research, said: "The findings from this substantial cohort add to a convincing body of evidence that genes influence characteristics that are ultimately reflected in educational performance.
"But it is equally important to stress that the researchers found that environments for students are also important and that the study does not imply that improvements in education will not have important benefits.
"For individuals living in the best and worst environments, this exposure is likely to make more of a difference to their educational prospects than their genes.
"Further research is needed to assess the implications of the findings for educational strategies."
Previous research indicates that large numbers of genes may be involved in academic ability, most of which have not been identified.
One study published in the journal Genes, Brain and Behaviour in 2010 found several gene variants linked to mathematical ability, but they only accounted for 2.9 per cent of the differences between individuals.
Mr Shakeshaft said the findings highlighted the importance of focused education that recognises strengths and weaknesses in individual children.
- PAA
