The highest proportion saying they were "very happy" was found in people with an IQ between 120 and 129 - 43% said they were very happy.
However, the highest proportion saying "not too happy" - 12% - was found in people with an IQ between 70 and 79.
Dr Angela Hassiotis said: "People in the lower end of the normal spectrum are more likely to consider themselves not happy."
The study said lower intelligence was linked to lower income, worse health and needing help with daily life, such as shopping or housework - all of which contributed to unhappiness.
Dr Hassiotis said: "There is some evidence that long term intensive strategies directed at young children from socially deprived backgrounds can have a positive impact not only on IQ, but also on wellbeing and life opportunities.
"Such interventions are likely to be costly, but the initial costs may be offset by future benefits such as a reduced reliance on state benefits and better mental and physical health."
Dr Jonathan Campion, a consultant psychiatrist and director of public mental health at the South London and Maudsley NHS Foundation Trust, said: "The study suggests that higher IQ appears to be associated with improved wellbeing, but that this relationship between IQ and wellbeing is partly due to higher IQ being linked with better income, health and less mental illness."
He added that the study was particularly helpful as it identified some of the factors that mediate the association between IQ and happiness, as well as highlighting interventions to prevent lower IQ leading to greater unhappiness.
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