For the large study, the researchers examined activity data of 91,105 people from the United Kingdom who were aged between 37 to 73 years.
A lower circadian amplitude denotes less distinction, in terms of activity levels, between active and rest periods of the day.
Daily circadian rhythm is controlled by a collection of neurons in an area of the brain called the hypothalamus.
They are also likely to feel more lonely and less happy, the study revealed.
The study can not say conclusively that body clock disturbances are what caused the mental risk, instead of the other way round.
The hypothalamus helps regulate a number of important behavioral and physiological functions such as body temperature, eating and drinking habits, emotional well-being and sleep, according to the National Institute of General Medical Sciences.
"While our findings can't tell us about the direction of causality, they reinforce the idea that mood disorders are associated with disturbed circadian rhythms, and we provide evidence that altered rest-activity rhythms are also linked to worse subjective wellbeing and cognitive ability", said Dr Lyall.
"Previous studies have been very small (in just a few hundred people), or relied on self-report measures (asking people what they think they do)".
"This is important globally because more and more people are living in urban environments that are known to increase the risk of circadian disruption and, by extension, adverse mental health outcomes".
The scientists studied people's circadian rhythms, which control functions such as immune systems, sleep patterns, and the release of hormones, to measure the daily rest-activity rhythms, also known as the relative amplitude. "But equally important is a pattern of exposing yourself to sunshine and daylight in the morning and doing activity in the morning or midday so you can actually sleep properly".
However, the researchers say it is still not certain whether an out-of-kilter body clock causes mental health problems, or if the mental health problems are causing disturbances to people's daytime and night-time cycles.
"The next step will be to identify the mechanisms by which genetic and environmental causes of circadian disruption interact to increase an individual's risk of depression and bipolar disorder", said Daniel Smith, a professor of psychiatry and senior author of the study. "My suspicion is that we might observe even more pronounced effects in younger samples, but that hasn't been done yet, to my knowledge". The team negated influences of other factors such as age, gender, season during which the test was taken, smoking status, socioeconomic status, past traumatic experiences from childhood etc. these could also have an influence on the mental health and thus had to be accounted for before any conclusions could be drawn, explain the researchers.
"It's an exciting time for this kind of research because it's beginning to have some real-world applications", Smith said.