The new rules, announced last December after a consultation, mean that ads that directly or indirectly promote HFSS products cannot appear in media aimed at children under 16, or where children under 16 make up at least 25% of the audience.
The ASA confirmed this would include any social media influencers with an audience that is over 25% children, if they are paid to promote HFSS products.
The ASA said if audience data was not available, it would assess the content and context of the ad and the surrounding media to determine whether it was likely to be targeted at children or to attract a significant child audience.
At the same time, the Committee of Advertising Practice is relaxing the rules around non-HFSS food and drink brands to allow them to use promotions, licensed characters and celebrities popular with children under 12. Previously, this was banned for all food and drink products except fresh fruit and veg.
This change could mean an increase in marketing of this kind by brands whose products are not HFSS, but were previously banned from doing it.
The question of which products are HFSS will be determined by the Department of Health nutrient profiling model.
James Best, chairman of CAP, said: "The tougher new advertising food rules are a significant and positive change designed to help protect the health and wellbeing of children. These measures demonstrate the advertising industry’s continuing commitment to putting the protection of children at the heart of its work.
"The new rules will alter the nature and balance of food advertising seen by children and play a meaningful part in helping change their relationship with less healthy foods."
The changes have been welcomed by industry representatives.
Ian Wright, director general of the Food and Drink Federation, said: "Two years ago, FDF announced its backing for major changes to the way food and drink is advertised, based on our belief that non-broadcasting advertising rules should be in line with the strict rules already in place for TV.
"HFSS food and drink ads have long been banned on children's TV, with under-16s today seeing far fewer of these ads than in recent years. As young people move away from traditional media towards new and social media, we feel it's important that ad rules keep up with this change."
Gavin Partington, director general at British Soft Drinks Association, said the the soft drinks sector had been a "driving force in pushing for further measures to support children’s health and wellbeing."
Richard Lindsay, director of legal and public affairs at the IPA, said the changes proved the UK’s regulatory system was able to balance the factors it needed to take into account.
"The new rules, which will apply across all non-broadcast media such as print, cinema and online – including social media – demonstrate that CAP is strong enough to take difficult decisions and flexible enough to implement them," he said.
"The changes are designed to protect children, one of the core principles of our industry’s self-regulatory system, and the IPA supports them."