The risk is greatest for those born very prematurely or less than 32 weeks' of gestation, according to the study that looked at medical records of more than 1.5 million people.
Compared with normal term babies, or those who born after a 40-week gestation period, they are three times more likely to be hospitalised for a psychiatric problem as an adult, the researchers found.
Their risk of bipolar disorder is increased more than seven-fold, while the chances of developing major depression and eating disorders are raised 2.9 and 3.5 times, they found.
However, experts stressed that the chances of a premature baby having a serious psychiatric problem remain small, as the vast majority of pre-term babies turn out healthy and normal -- famous examples include Sir Winston Churchill and Albert Einstein, the Daily Telegraph reported.
For the study, reported in journal Archives of General Psychiatry, the researchers looked at 1.5 million Swedish birth and medical records from 1973 and 1985.
Every child admitted to hospital with a first episode of a psychiatric disorder by 2002 was identified.
More From This Section
The researchers found that psychosis was 2.5 times more likely for pre-mature babies, severe depression three times more likely, and bipolar disorder 7.4 times more likely for those born before 32 weeks.
Babies born between 32 to 36 weeks also had an increased risk of mental health disorders, though too a lesser extent.
Researchers believe the pattern is due to the impact of being born prematurely on early brain development. However, it is not clear why some kids are affected and others are not.
Lead study author Dr Chiara Nosarti from the Institute of Psychiatry at King's College London, said: "We found a very strong link between premature birth and a range of psychiatric disorders. Since we considered only the most severe cases that resulted in hospitalisation, it may be that in real terms this link is even stronger.
"However, it is important to remember that even with the increased risk, these disorders still only affect 1 per cent to 6 per cent of the population."