Conditions range from depression and anxiety, to ADHD (attention-deficit/hyperactivity disorder) and schizophrenia.
The findings published in the journal JAMA Psychiatry are based on 1.3 million Danish children who were monitored from birth to 18 years of age.
Of those studied, 14.6 per cent of girls and 15.5 per cent of boys were diagnosed with a mental illness before the age of 18, with anxiety the most common diagnosis for girls and ADHD for boys.
The researchers also found that identifying these illnesses in girls could be missed due to “delayed detection”, whereby girls tend to be diagnosed much later.
Girls were found to be more susceptible to schizophrenia, obsessive-compulsive disorder (OCD) and mood disorders than boys, but boys were found to be more prone to mental illness at a younger age, with ADHD peaking at age eight for boys and 17 for girls.
The trend also applied to intellectual disability and other developmental disorders in boys, each tending to start at the age of five compared with 14 and 16 years for girls.
Eating disorders were also much higher in girls (1.8 per cent) than boys (0.28 per cent).
Corresponding author Professor Soren Dalsgaard, a child psychologist at Aarhus University in Denmark, said: “Worldwide, this nationwide study is the first, to our knowledge, of the incidence of the full spectrum of diagnosed mental disorders in childhood and adolescence.
"These findings suggest precise estimates of rates and risks of all mental disorders during childhood and adolescence [and] are essential for future planning of services and care and for research,” he added.
In October, the UK government’s first State of the Nation report on children’s wellbeing revealed that nearly one in five young people said they were not happy with their lives.
One of the key reasons for reported unhappiness or poor mental wellbeing among the respondents was bullying, including cyberbullying, with girls more likely to report incidents of cyberbullying than their male counterparts.
And in July, a study of NHS trusts found child referrals to mental health clinics in the UK rose by nearly 50 per cent over three years.
Mental health experts and teachers described the situation as a "crisis", with school staff even seeing youngsters “headbutt walls on a daily basis”.
The World Health Organisation has emphasised the important of age and sex-specific data on child mental health.
“Knowledge about the epidemiology of mental disorders in children and adolescents is essential for research and planning of health services,” said Professor Dalsgaard.