Counties in England will receive £294.8m, said culture secretary Jeremy Hunt on Tuesday (16 August). Scotland will receive £68.8m.
Funding is part of a £530m government investment to ensure the UK has the best superfast broadband network in Europe by 2015.
Mr Hunt said 90% of homes and businesses would have access to superfast broadband, with everyone in the UK having access to at least 2Mbps.
But local authorities and the Scottish government will be expected to help ensure the target is met.
In England, county councils and local enterprise partnerships will lead broadband roll-out in their area.
They will be expected to draw up an effective delivery plan, and match the government's investment with European, their own or private funds.
A table showing funding allocations across England can be downloaded by clicking here (153kb pdf).
The Scottish Government will consider how best to use the funds in Scotland.
"I am absolutely determined that the UK will have the best superfast broadband network in Europe by 2015 – one that we all benefit from," said Mr Hunt.
"Fast broadband is absolutely vital to our economic growth, to delivering public services effectively, and to conducting our everyday lives."
"But some areas of the UK are missing out, with many rural and hard-to-reach communities suffering painfully slow internet connections or no coverage at all.
Mr Hunt said the government was not prepared to let some areas get left behind in the digital age.
"The government is investing £530 million of public money to help bring broadband to every home and business in the UK.
"We are doing our part – it is now up to local authorities and the Scottish government to do their bit."
The government said the funding was allocated to areas where the market would fail to deliver superfast broadband to enough premises on its own.
Rural affairs secretary Caroline Spelman said: "In the 21st century, it is unthinkable that parts of England still do not have access to broadband.
"Rural communities should never be overlooked when it comes to services that most of us take for granted.
Decent internet access was vital for the social and economic growth of rural towns and villages.
It was essential for modern businesses, as well as for homes and schools, said Mrs Spelman.
Allocations for Wales and Northern Ireland have already been announced.