The study of 4,350 pupils, commissioned by the Welsh Assembly Government(WAG) to assess its free breakfast scheme, found no educational benefits.
However, Dr Simon Murphy, from Cardiff University's Institute of Society, Health and Ethics, said the multi-million pound initiative had encouraged children to eat more healthily.
"Free healthy school breakfasts are good for improving nutrition in children but do not prove effective in terms of education," he said.
Teachers reported improved concentration and behaviour but this had not been proved by the study.
Pupils who either had or had not eaten free breakfast were tested on word recall and word search tasks. Teachers were also asked to rate the behaviour of pupils selected randomly by researchers, and parents answered questionnaires.
"We particularly looked at hyperactivity and attention but again, on that measure, we did not find any effect in terms of that behaviour," Dr Murphy said.
"All the teachers said there were improvements in behaviour but we did not find that in our test."
However, the survey recommends the WAG continues with the scheme on the grounds that it promotes healthy eating.
Dr Murphy said more research was needed and the survey found areas where pupils had previously had breakfast at home were more likely to take-up the free breakfast scheme. Around 20% of pupils in the study skipped breakfast and 41% had it at school.
"They are now eating more healthy food, more wholemeal bread and grains," he pointed out.
"Dietary habits originate in childhood. This is effective as a dietary health intervention but does not appear effective as an educational intervention. The WAG has done an evaluation which is rarely done. Now we will learn what is effective."
Teachers and teaching unions are divided. Teachers say being hungry affects attention and behaviour but some head teachers said schools should not have to provide breakfast.
The National Association of Schoolmasters Union of Women Teachers(NASUWT), a leading union warned as far back as three years ago that the Ł2.9m spent annually might be better spent directly on education.
It says that free breakfasts might be going to the wrong people and that those who most needed it could be losing out.