
Currently, the ASA’s online remit only includes ads in paid-for space and sales promotions, and it has been unable to act on thousands of complaints it has received since 2008.
However, from next year, advertisers will be responsible for ensuring that marketing communications on their own websites have the same high standards as in other media, such as newspapers and TV.
The new powers focus on selling messages, but to protect freedom of speech online, they exclude editorial content and material related to ideas or causes, except for direct solicitations of donations for fundraising.
Non-compliance sanctions will include the removal of paid-for search advertising, with the agreement of search engines.
The ASA will also name and shame any advertiser that continually flouts the regulations by putting up its own online ads.
The extension of the powers is funded by a 0.1% levy on search ads booked through media and search agencies, replicating the ASA's existing funding mechanism in other media.
The levy will be supplemented initially by an undisclosed amount of seed capital from Google.
Former Labour culture secretary and ASA chairman, Lord Smith, said: "This remit has the protection of children and consumers at its heart. We have received more than 4,500 complaints since 2008 about marketing communications on websites that we could not deal with."