Pupils who eat breakfast are up to twice as likely to do well at school as those who do not, according to the biggest study of its kind.
Researchers found a "significant link" between eating breakfast and performing above average on teacher assessment scores.
There was also a strong link between eating a healthy breakfast - such as cereal, bread, dairy or fruit - and doing well at school.
There was no such link for the one in five pupils who ate junk for breakfast, such as crisps or sweets.
The study on around 5,000 pupils from more than 100 primary schools was led by a team at Cardiff University.
It involved asking pupils aged nine to 11 what they ate for breakfast and during the rest of the day, and following their educational progress six to 18 months later.
The team found that a good breakfast was strongly linked to performing above average on Key Stage 2 teacher assessments, while there was also a link for those pupils who carried on eating fruit and veg at other times of day.
Dr Graham Moore, who worked on the study, said: "We analysed links between whether young people were eating breakfast and the quality of that breakfast.
"There's a significant association between eating breakfast and doing well, but there is also a link between a healthy breakfast and doing well.
"The odds of achieving an above average teacher assessment score were up to twice as high for those pupils who ate breakfast.
"The odds of scoring above average was between 50% and 100% higher if any breakfast was eaten."
Dr Moore said it did not matter whether pupils ate breakfast at home or during a breakfast club at school.
"The main thing is to make sure they have a breakfast," he said.
During the study, pupils were asked to list all the food and drink they consumed over a period of just over 24 hours, including two breakfasts.
Hannah Littlecott, lead author of the study, said: "While breakfast consumption has been consistently associated with general health outcomes and acute measures of concentration and cognitive function, evidence regarding links to concrete educational outcomes has until now been unclear.
"This study therefore offers the strongest evidence yet of links between aspects of what pupils eat and how well they do at school, which has significant implications for education and public health policy - pertinent in light of rumours that free school meals may be scrapped following George Osborne's November spending review.
"For schools, dedicating time and resource towards improving child health can be seen as an unwelcome diversion from their core business of educating pupils, in part due to pressures that place the focus on solely driving up educational attainment.
"But this resistance to delivery of health improvement interventions overlooks the clear synergy between health and education. Clearly, embedding health improvements into the core business of the school might also deliver educational improvements as well."
Chris Bonell, professor of sociology and social policy at the University College London Institute of Education, said: "This further emphasises the need for schools to focus on the health and education of their pupils as complementary, rather than as competing priorities.
"Many schools throughout the UK now offer their pupils a breakfast. Ensuring that those young people most in need benefit from these schemes may represent an important mechanism for boosting the educational performance of young people throughout the UK."
A spokeswoman for the Department for Education said: "We are determined to give every child, regardless of their background, the very best start in life.
"We are already spending £1.1 million to provide breakfast clubs in schools to help children start the day with a nutritious meal, supporting academic attainment and saving parents money.
"We have also provided significant financial support to schools to help them deliver universal infant free school meals and the new School Food Standards mean pupils of all ages are eating good food that fuels their learning.
"For the first time, learning about food is statutory for every pupil up to the age of 14, and we have reformed the national curriculum to include new content on food, nutrition and healthy eating, as well as how to cook a repertoire of dishes, sowing the seeds for healthy eating for life."