Schoolchildren will be given better access to NHS mental health workers in an attempt to stop depression and anxiety from becoming "entrenched" and "destroying" their lives.
Prince Harry was praised for his bravery after revealing in an interview with The Telegraph that he had sought counselling to help come to terms with the death of his mother.
Theresa May hailed his intervention and said it would help "smash the stigma" surrounding mental health and make thousands of people realise that they are "not alone".
Ministers are now examining plans to station NHS professionals in secondary schools on a full-time basis for a green paper on young people and mental health that will be unveiled later this year.
They want to "normalise" discussions about mental health in school to tackle concerns that rates of depression and anxiety among teenagers have increased by 70 per cent in the past 25 years.
The Duke of Cambridge, Prince Harry's brother, praised high-profile public figures for speaking out and said that no one should try to keep a "stiff upper lip" at the expense of mental health.
The Duke said that the idea that successful, strong people do not suffer from mental health issues is false. "We all do," he said. "It's just few of us speak about it".
The Prince disclosed in his interview with The Daily Telegraph that he had endured two years of "total chaos" while struggling in his late twenties to come to terms with losing his mother Diana, Princess of Wales.
He said that the Duke had tried to help him, saying: "This is not right, this is not normal, you need to talk about stuff, it's OK."
He spoke to The Telegraph’s Bryony Gordon for the first episode of her podcast, Mad World, in which she will interview high-profile guests about their mental health experiences.
The Prince and his brother and sister-in-law, the Duke and Duchess of Cambridge, have together driven Heads Together, a charity which promotes good mental well-being.
The Prince's decision to speak out was also lauded as "a true turning point" by Mind, the mental health charity, while the campaign group Time to Change said he "will have helped change attitudes" by sharing his experiences.
His comments prompted politicians and other public figures to open up about their own experiences with mental illness, with one Labour MP describing the "chaos and madness" he felt after losing his sister.
Dickie Arbiter, the Queen's former press secretary, said that Prince Harry and the Duke and Duchess of Cambridge "have done for mental health what Diana, Princess of Wales, did for HIV Aids - create awareness and remove stigma".
My way of dealing with it was sticking my head in the sand, refusing to ever think about my mum, because why would that help?
The Prime Minister yesterday led praise for Prince Harry's "bravery" and said that mental health was an "everyday concern for all of us".
She said: "Mental health problems affect people of all ages and all backgrounds. The bravery of those in public positions who speak out about their experiences help smash the stigma around mental health and will help thousands of people to realise they are not alone.
"If we are to tackle this injustice, we must forge a new approach that recognises our responsibility to each other, and make mental illness an everyday concern for all of us and in every one of our institutions."
In January Mrs May unveiled plans to offer secondary schools "mental health first-aid training" to help teachers identify pupils who need support give them counselling.
She said at the time: "We know that mental illness too often starts in childhood and that when left untreated, can blight lives, and become entrenched."
The new proposals for the Green Paper go significantly further and suggest that qualified NHS medical health workers should be based in larger secondary schools, or provide support for networks of smaller schools.
Jeremy Hunt, the Health Secretary, last year hinted at the new approach as he said that the NHS is "letting down" families by failing to do more to help children.
He said: “I think we are letting down too many families and not intervening early enough when there is a curable mental health condition, which we can do something about when a child is eight or nine, but if you leave it until they are 15 or 16, it’s too late.
"I think this is possibly the biggest single area of weakness in NHS provision at the moment. There are too many tragedies because children develop eating disorders or psychosis or chronic depression, which is then very difficult to put right as they get older.”
He said that he wants NHS children and adolescent mental health services [CAMHS] to work more closely with schools. “There are big problems with the capacity in CAMHS services, but it’s not just there, but what happens in schools. Very few schools have a full-time CAMHS worker,” he said.
Paul Farmer, chief executive of Mind, described Prince Harry's interview as "inspiring".
"It shows how far we have come in changing public attitudes to mental health that someone so high-profile can open up about something so difficult and personal," he said.
"We know that this will have a huge impact on people who are still struggling in silence with their mental health - every time someone in the public eye speaks up we know that it encourages ordinary members of the public to do the same."
Sue Baker, director of Time to Change, said: "Prince Harry sharing his experiences of mental health issues and the counselling he sought as a result of losing his mother will have helped change attitudes, not just at home but also overseas.
"It was a dream of mine 20 years ago that we'd see the royal family join sports people, music stars, politicians and business leaders as well as everyday people in sharing their mental health experiences in all sorts of communities.