The report, presented at the conference of the British Sociological Association, also shows that those who enjoy PE at school are markedly more likely to report being happy in general.
Those whose parents enjoyed good health also reported higher levels of happiness in their daily lives.
But when it comes to eating, the findings are less likely to please health chiefs.
The results suggest that eating fruit and vegetables has little positive effect and possibly even makes children slightly less happy overall.
Meanwhile, those allowed to eat sweets and sugary snacks in safe measure also emerged as having higher levels of wellbeing than those for whom they are forbidden.
While children afforded more than five hours of television a day scored lower than those who watched around an hour, so did those who did not see any.
The report, based on data provided by the Millennium Cohort Study, which tracks the lives of thousands of children born in 2000, highlighted how 40 per cent of those who said they liked PE "a lot'', separately said that they were happy "all the time".
Less than a quarter of those who said they disliked PE also spoke of always being happy - strengthening links between health and happiness.
But in the children's assessment of their feelings when linked to their diets, a more complicated picture emerged.
There was no significant difference in well-being between those allowed crisps, cakes, biscuits, sweets, chocolate or sugary drinks between meals and those who were not.
Meanwhile, 38 per cent of those who said they were happy "all the time" ate no fruit and vegetables. Thirty-six per cent of the happiest children had one or two portions and only 35 per cent had three or more.
Jenny Chanfreau, the study's lead author, said the difference was not statistically significant, but showed that it cannot be claimed that eating greens will make children happier overall.
"This is not to say that eating healthily isn't good for you, it is just not linked with happiness as reported by seven-year-olds," she said.
She said the most striking finding was that moderation, not prohibition, was linked with general wellbeing.