While the ban on lighting up in places like pubs and restaurants had already been proven to protect adults from the effects of passive smoking, a team led by Edinburgh University researchers studied the effect of the laws on the health of children in different countries for the first time.
It was found that, while the impact of anti-smoking laws varied between countries, the effect on child health was described as "very positive" overall.
Scotland was the first area of the UK to ban smoking in public places in March 2006, followed a year later by England.
The research, published today in medical journal The Lancet, found the laws had contributed towards a one-tenth fall in premature births.
There was also a drop in the number of hospital attendances for childhood asthma attacks of 10%. The team looked at over 2.5 million births and almost 250,000 hospital attendances for asthma attacks.
Researchers said they hoped the study, which looked at data from North America and Europe, would prompt other countries to follow Scotland's lead and embrace a ban on smoking in public places.
Less than one-sixth of the world's population are currently protected by anti-smoking laws, meaning 40% of children are regularly exposed to passive smoking.
Professor Aziz Sheikh, co-director of the Centre for Population Health Sciences at Edinburgh University , said: "This research has demonstrated the considerable potential that smoke-free legislation offers to reduce pre-term births and childhood asthma attacks.
"The many countries that are yet to enforce smoke-free legislation should in the light of these findings reconsider their positions on this important health policy question."
While 13,500 people still die every year as a result of smoking, the law has been credited with bringing significant health benefits, while also changing attitudes towards tobacco.
The latest figures show that, in the two years to March 2013, 236,000 smokers attempted to quit in Scotland, with a 38% success rate after one month.
Passive smoking can cause babies to be stillborn or born prematurely and is linked to birth defects, asthma and lung infections. Studies have also suggested that being exposed to second-hand smoke during childhood may have long-term health implications, contributing to heart disease and diabetes.
The study, which also involved researchers from Maastricht University, Hasselt University, Harvard Medical School and Brigham and Women's Hospital, suggests the fears it would lead to more people smoking at home were unfounded.
Lead researcher, Dr Jasper Been of Edinburgh University's Centre for Population Health Sciences, said: "Our research shows that smoking bans are an effective way to protect the health of our children."