The government has published its White Paper setting out the corporation's future functions, role and structure.
The licence fee will remain until 2016 and the BBC governors will be scrapped.
Culture Secretary Tessa Jowell said the BBC must make popular quality services. Director general Mark Thompson welcomed the "massive vote of confidence".
The paper will pave the way for the renewal of the BBC's Royal Charter, which expires this year.
As well as the corporation's traditional aims to "inform, educate and entertain", the government has set it six new purposes:
Building digital Britain
Ms Jowell said there was strong public support for those purposes - but licence-fee payers did not want "an overdose of worthiness".
"So the White Paper makes entertainment central to the BBC's mission," she told the House of Commons.
"The BBC should continue to take fun seriously, ingraining entertainment into all its services," she said.
"We are optimists about the BBC but it cannot take its position for granted."
Life on Earth, I'm Sorry I Haven't A Clue and Strictly Come Dancing were among the programmes singled out for praise for their creativity in the White Paper.
The licence fee would remain as the "least worst" way to fund the corporation, the document said.
But this would be reviewed during the next decade, with other methods - such as subscriptions - to be considered.
The government will also examine whether to give licence fee money to other public service broadcasters, such as Channel 4.
The level of the licence fee in the coming years is being decided in a separate negotiation and will be announced later this year.
The BBC wants the fee to rise by 2.3% above inflation every year.
The White Paper also confirmed plans to create a BBC Trust in place of the current system, which makes governors "both champion and judge", it said.
The Trust is intended to be more removed from BBC management and more accountable to licence fee payers.
There would be an "unprecedented obligation to openness and transparency", the White Paper said.
Ms Jowell said the Trust would become "the licence fee payer's voice".
But shadow culture secretary Hugo Swire criticised the "cosy" BBC Trust plans and called the White Paper "a huge missed opportunity for change and innovation".
The government says all BBC content must display at least one of these characteristics
Mr Swire said: "It was supposed to provide us with a springboard to the new digital age.
"But it is not so much a launching pad as a holding pen."
Every part of the BBC will be given its own service licence, setting out exactly what it does, so the public and commercial rivals know what to expect.
The BBC Trust will have the power to review the licence if it believes the service is not fulfilling its role.
New services or "significant" changes to existing services will be subject to a public service test before being approved by the Trust.
This will weigh up their public value against how much they hurt their rivals, with media regulator Ofcom carrying out a market impact assessment in each case.
BBC Radio 4's I'm Sorry I Haven't a Clue was praised in the White Paper
ITV chief executive Charles Allen welcomed the appointment of the BBC Trust but said: "The BBC's funding must be proportionate to its needs and should not be able to stifle competition and innovation."
Paul Brown, the chief executive of the Commercial Radio Companies Association, said he had some reservations.
"I think the chairman of the Trust, Michael Grade, has got his work cut out to make sure that it is trustworthy and is seen to be impartial," he said.
BBC director general Mr Thompson called the White Paper a "blueprint for an independent BBC" and welcomed the innovation of the BBC Trust.
He said: "Ultimately, the Trust will be sovereign, what they say goes."
BBC chairman Michael Grade said this "finally resolves the schizophrenic lives of governors at the BBC".
"This is an unprecedented shake up of the BBC's governance system which is long overdue in my estimation and in the judgment of my present colleagues of the board about to be abolished," he added.