Professor Lord Richard Layard, from the London School of Economics, believes the central purpose of schools should be to teach "the secrets of happiness".
He is calling for a new generation of teachers specialising in what is known as "emotional intelligence".
Teachers' leaders say they do all they can to promote children's well-being and the timetable is already crowded.
Lord Layard said people were no happier today than they were 50 years ago and that there had been a sharp fall in the numbers saying they trusted other people.
"We have had endless experiments trying to teach people not to take drugs or drink which have failed.
"We need to go down the route of giving values to people. There are scientifically-evaluated programmes which have halved depression in teenagers."
He said schools should follow programmes in "emotional intelligence", so that children could learn how to manage their emotions and look at attitudes to work and money.
The ideas could be made part of lessons in personal, social and health education, he said.
John Bangs of the National Union of Teachers said: "Our members recognise the diagnosis but will be concerned by the solution.
"Teachers spend a lot of time trying to ensure that their pupils are happy people, however, schools are test and exam factories these days.
"If schools are going to spend more time on developing ethos and encouraging pupils to be confident and happy then less time needs to be spent on lessons."
Wellington College introduced a programme of happiness or well-being lessons for older pupils last autumn.
The independent school collaborated with the Well-Being Institute of the University of Cambridge to devise the programme.
The school's website says the aim is to equip children "with an understanding of what makes lives thrive and flourish, and how they can improve their chances of experiencing happiness, good health, a sense of accomplishment and lasting companionship.
"The lessons should help them cope better during their teenage years, both in and out of school, and later at university."
The lessons are held once a fortnight throughout the school year.
Anti-bullying campaigners believe teaching children about their emotions will help improve behaviour in schools.
Emma-Jane Cross, of the charity Beatbullying said: "Teaching children emotional intelligence is central to the successful prevention of bullying behaviour all through their lives.
"We have seen this work in our bullying prevention programme for primary schools. After working with Beatbullying, schools report a significant reduction in bullying and disruptive behaviour of, on average, 40%."
Should happiness be taught in schools? Could teaching pupils lessons in emotional intelligence help tackle issues like bullying?
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Also See:IQ Is Only Half The Picture: Cultivating your Child's Emotional Intelligence - Part 3
Teaching children how to be happy