Fresh restrictions are also planned to govern their use of customers' data, and to prevent the firms ranking their own services above competitors' in search results and app stores.
The measures are intended to overhaul how the EU regulates digital markets.
Large fines and break-ups are threatened for non-compliance.
It is proposed that if companies refuse to obey, they could be forced to hand over up to 10% of their European turnover.
And "recurrent infringers" are warned that they could be made to divest "certain businesses, where no other equally effective alternative measure is available to ensure compliance".
The two new laws involved - the Digital Services Act and the Digital Markets Act - have yet to be passed, so would only come into force after the Brexit transition period has ended.
The UK's own regulator - the Competition and Markets Authority - announced its own plans to place limits on the tech giants last week, and ministers have just detailed how they plan to tackle online harms.