The government has given Ofcom two years to implement the broadband Universal Service Obligation (USO).
This means that by 2020, everyone in the UK will have a legal right to an affordable connection offering speeds of at least 10Mbps.
BT had volunteered to deliver universal high-speed broadband to all areas of the UK, as an alternative to regulation.
Under BT's offer, which would have been primarily delivered by Openreach, many premises would have received speeds substantially faster than 10Mbps, thereby rendering the USO unnecessary.
However, ministers rejected this option, as only a regulatory USO would offer "sufficient certainty and the legal enforceability" that is required to ensure high-speed broadband access for the entire country by 2020.
Indeed, the government stated that while 95 per cent of the UK already has access to superfast broadband, the USO will provide a "digital safety net" for those living in remote and hard-to-reach areas.
Margot James, the Digital Minister, commented: "In the 21st century, accessing the internet is a necessity not a luxury.
"We are building a Britain that is fit for the future, and we’re now putting high-speed broadband on a similar footing as other essential services like water and phone lines."
The government believes 10Mbps is a suitable speed for the USO as this is what Ofcom advises is the speed required for a typical household with internet access.
However, ministers have pledged to keep the USO minimum speed under review and said they expect it to be increased over time.
The Department for Digital, Culture, Media & Sport added that the government is now working with Ofcom to develop processes to ensure the USO is implemented "as quickly as possible".