The BBC is to move factual programming from the Mailbox in Birmingham to Bristol under proposals for a "smaller" corporation.
Cutbacks will also see the BBC lose thousands of jobs, sell off offices and show more repeats.
Some shows, such as Doctors and The Archers will continue to be produced by the BBC in Birmingham, while the city's Asian Network radio station, which was previously threatened with closure, will lose a third of its "service licence budget reduction".
The "Delivering Quality First" proposals, announced by Director General Mark Thompson, include "a small reduction" in new programmes on BBC One, which will be replaced by repeats, fewer chat shows and panel shows on BBC Two and digital channels BBC Three and Four will become feeder channels for BBC One and Two respectively.
The report states: "Factual programming for BBC television and Radio 4 would be moved out of Birmingham and consolidated largely to Bristol and Cardiff, though television production investment with independent producers in the Midlands would increase. Substantial network television drama (e.g., Doctors, Land Girls) and radio drama (The Archers) would continue in Birmingham alongside the BBC’s local and regional services."
About 2,000 jobs are expected to go by 2016, with about 1,000 more staff moving to the new BBC base at Media City in Salford.
There will be "a phased but full exit for the BBC's public services from their current home in West London" including its White City offices.
The plan is expected to lead to savings of £670 million a year by 2016/17.
Mr Thompson said: "It's a plan for a smaller BBC, but a BBC which uses its resources more effectively."
The BBC HD channel will be closed and replaced with an HD version of BBC Two and all new daytime shows will be moved to BBC One with more repeats on Two.
There will also be less original programming on radio, with cuts to comedy on Radio 2 and Radio 5 Live and fewer lunchtime concerts on Radio 3.
Some radio stations will also share news bulletins.
The corporation is holding a series of meetings with its staff across the UK to reveal details of its Delivering Quality First initiative.
The BBC committed itself to saving billions of pounds from its budget after the annual licence fee was frozen at £145.50 for six years.
The report states that BBC bosses considered "the possibility of shutting one or more services entirely" but rejected the idea on value-for-money grounds.
It states: "The decision to share Formula One motor-racing rights with BSkyB, for example, will save the BBC more cash between now and the end of the Charter than we would have saved by shutting one of the smaller TV channels."
The sports rights budget will see a 15% cut, which includes the decision to share Formula One rights.
The National Union of Journalists condemned the spending and job cuts, saying they had come on top of many years of other cutbacks across news and programme-making.
The union said more than 7,000 jobs had been lost at the BBC since 2004, adding that the situation "isn't sustainable".
At a time of falling pay and job uncertainty, staff were being asked to bear the burden of this deal, with cuts to redundancy terms, re-grading being proposed and a move to statutory redundancy consultation periods and performance related pay, said the NUJ.
General secretary Michelle Stanistreet said: "This is a watershed moment in the BBC's history - the reality is that the BBC will not be the same organisation if these cuts go ahead.
"You cannot reduce budgets by 20% and pretend that the BBC will still be able to be a world-class broadcaster. Quality journalism and programming is inevitably going to be diluted.
"If the BBC presses ahead with these changes strike action across the corporation seems inevitable."
Gerry Morrissey, general secretary of the technicians' union Bectu, said: "They are destroying jobs, and destroying the BBC."
Mr Morrissey accused Mr Thompson of doing the Government's "dirty work" by making such big cuts in spending and jobs, accusing the corporation of "salami slicing".
The BBC said it will build on its current efficiency programme, which has already seen savings of more than £1 billion since 2008/09, to release a further £400 million of savings per year by 2016/17.
The BBC Trust said it had been assessing this work with the help of independent advisers, adding that the savings will be achieved by a more flexible workforce which "reduces duplication of expertise", streamlining the use of technology, continuing to reduce the number of senior managers and increasing production outside London.
A series of meetings will be held at BBC offices across the UK today when staff will be told how the cuts will affect them, while union leaders will meet senior management later.