Professor Steven Blair, from the University of South Carolina, said a "greater emphasis" had to be placed on physical activity to prevent the problem reaching US proportions.
He suggested exercise could be "prescribed" to patients by their doctors or other health professionals.
He was speaking ahead of a major conference in Edinburgh.
The event has been organised by the Royal College of Physicians of Edinburgh and the Royal College of Surgeons of Edinburgh.
It will focus on sports and exercise medicine ahead of the Commonwealth Games in Glasgow in July.
Prof Blair, from the university's Arnold School of Public Health, claimed physical inactivity had become "the biggest public health challenge of the 21st Century" and said people must consider their levels of activity as well as their diet.
He said much of the internationally-published scientific literature on the causes of obesity was "flawed", arguing that it placed "an over-emphasis on dietary intake, at the expense of measuring the positive effect of physical activity".
Prof Blair said: "Obesity rates continue to rise and in international obesity terms, Scotland is not far behind the US. If we wish to prevent levels in Scotland reaching that of the US, greater emphasis has to be placed on exercise.
"This could involve creative solutions such as considering the provision of exercise advice, or indeed the prescribing of exercise to patients by doctors and other health professionals.
"We have to become more active if we are to stop collectively sleepwalking into obesity."
Prof Blair added: "In simple terms, we are talking about changing the mind-set from thinking 'I must go on a diet' to 'I must become more active'.
"By bringing together leading experts in the field of sports medicine in the year of the Commonwealth Games, we hope to shine a light on developments in sports medicine, stimulate wider awareness about the many benefits of physical activity and creative thinking about this can be applied to improve health."
The conference will hear from a number of other speakers including Scotland's Chief Medical Officer Sir Harry Burns, former Scotland manager Craig Brown and ex-footballer Pat Nevin.
Scots risk "sleepwalking into obesity" if they do not take more exercise, an expert has warned.