Developer RWE Innogy is pulling the plug on the 240-turbine Atlantic Array project, the Department of Energy and Climate Change (DECC) told the BBC.
The scheme, which had not yet received the go-ahead, had attracted criticism, with environmentalists worried about its impact on marine wildlife in the Bristol Channel.
RWE Innogy said it was "not the right time" for the project.
The Atlantic Array was planned in an area of 200 sq km (77 sq miles) about 16.5km (10 miles) from the north Devon coast, 22.5km (14 miles) from south Wales coast and 13.5km (8 miles) from Lundy Island nature reserve.
The turbines would have been 220m (720ft) tall and capable of producing 1,200 megawatts of electricity - enough for up to 900,000 homes, the developer has said.
RWE said it was "not viable... to continue with development in the Bristol Channel Zone".
RWE's director of offshore wind, Paul Cowling, said: "This is not a decision we have taken lightly.
"However, given the technological challenges and market conditions, now is not the right time for RWE to continue to progress with this project."
DECC told the BBC the scrapping of the scheme was a matter for the developer, but the decision "was made on purely technical grounds and reflects the many complex challenges of constructing offshore wind farms".
But BBC South West political editor Martyn Oates said: "Sources have told us that this will not go ahead because of problems in financing it.
By Roger HarrabinEnvironment analyst
The collapse of the Atlantic Array project highlights the current chaos in energy policy.
RWE and other firms are complaining that energy has become a political football, with Labour trying to freeze prices and the Conservatives apparently dismissing renewables subsidies as "green crap".
Investment in new large scale projects like offshore wind farms has dried up.
Developers are waiting to see what price they will be able to sell their power. Some developers also want to see the outcome of further details of the Energy Bill, which will not be decided until sometime next year.
The industry is angry that the government has asked it to invest Â£100bn renewing generating capacity in the UK, whilst creating political conditions which they say make that investment impossible.
There is an irony, too. The eventual cost of power will partly depend on how cheaply developers can borrow capital. Lenders demand higher rates of interest if there's uncertainty. So by arguing about bringing down bills, the politicians may inadvertently be forcing them up.
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"Just last week, [green energy group] Regen SW said that the government's recent announcement that it is going to cut back on green levies to support renewable energy was already undermining investment in the region and putting jobs at risk.
"And in terms of investment and jobs, this is a really big project, the company (RWE) says it would provide thousands of jobs."
Friends of the Earth's head of campaigns, Andrew Pendleton, said: "The government's wanton green-bashing is starting to cost jobs and threaten the future security of our energy supply.
"The UK has some of the finest offshore clean energy resources in the world and harnessing it is becoming cheaper.
"But anti-green ideology at the heart of the coalition is sending the development of world-beating clean power into reverse."
But DECC told the BBC: "The UK still expects to deploy significant amounts of offshore wind by 2020 and we remain well placed to meet our 2020 renewable energy target."
Derek Green, manager of Lundy Island, said: "If it's true then we are absolutely delighted.
"It is fantastic news for tourism and wildlife in the Bristol Channel and in particular for Lundy."
Three steps to build a wind farm
Lundy's owners, the Landmark Trust, have spent the last 40 years "preserving a special way of life".
"We were concerned that by bringing development so close to the island that it would overwhelm it," said Mr Green.
"There are many turbines near Landmark Trust properties which we haven't opposed.
"But we have always said that offshore wind farms should be built offshore and this suite was in the middle of the Bristol Channel.
"We all need electricity, but there are more appropriate places."
Other critics also welcomed the move.
Steve Crowther, from local campaign group Slay the Array, said: "This was clearly an ill-conceived scheme in completely the wrong place."
Plans for a huge wind farm off the north Devon coast have been shelved.