The acts also make it illegal for adults to smoke in a car where there is a child under 12, and pave the way for picture warnings such as diseased lungs on cigarette packs.
"The new laws will have dramatic, important and far-ranging effects on public health and the tobacco industry's marketing activities," said council director Yussuf Saloojee.
The acts were passed by Parliament in 2007 and 2008.
Saloojee said fines for smoking or allowing smoking in a non-smoking area increased with immediate effect.
Illegal in public places
The fine for the owner of a restaurant, pub, bar or workplace that breached the smoking laws was now a maximum of R50 000, and for the individual smoker R500.
Smoking was now illegal in "partially enclosed" public places such as covered patios, verandas, balconies, walkways and parking areas.
Nor was it allowed on premises, including private homes that are used for commercial childcare activities, or for schooling or tutoring.
The tobacco industry was no longer permitted to hold "parties" or use "viral" marketing to target young people.
The sale of tobacco products to and by people under 18 years was prohibited, as was the sale of confectionery or toys resembling tobacco products.
22% of South Africans smoke
The use of picture-based health warnings on tobacco packaging would come into effect only later this year, because the health ministry was still finalising regulations.
Also in the pipeline were rules to keep smoking away from entrances to buildings, and restrict it in sports stadiums, railway platforms, bus stops and outdoor dining areas.
Saloojee said tobacco killed 44 000 South Africans every year, three times more than vehicle accidents.
"Our efforts to reduce the death toll will be helped by the new legislation," he said.
Prevalence of adult smoking in South Africa had fallen by a third in the past decade, from 32% in 1995 to 22% in 2006.