The TV licence fee, which funds the BBC, is to be frozen for six years at £145.50, the chancellor has confirmed.
The BBC will also take over the cost of the Foreign Office-funded World Service, BBC Monitoring and some of the costs of Welsh language TV channel S4C.
All the changes mean a 16% real terms cut in BBC funds over six years.
BBC director general Mark Thompson said it was "a realistic deal", but the National Union of Journalists said the BBC should have fought the plans.
George Osborne told the Commons that changes in funding amounted to "£340m of savings a year for the Exchequer by 2014-15".
"To ensure that the cost of these new obligations is not passed on to the licence fee payer, the BBC has agreed a funding deal for the full duration of its charter review," he said.
The arrangement was to freeze the licence fee for the next six years, he added.
"This deal helps almost every family and is equivalent to a 16% saving in the BBC budget over the period, similar to the savings in other major cultural institutions."
As part of the deal, the BBC says it will now part-fund S4C "along similar principles to the BBC Alba service in Scotland".
BBC Alba - the Scottish Gaelic language service - is funded by the corporation in partnership with the Scottish government.
The Department for Culture, Media and Sport (DCMS) currently funds S4C to the tune of just under £100m a year.
The government also funds the World Service and picks up part of the cost of BBC Monitoring, which monitors, translates and analyses media coverage from around the world.
Mr Thompson said: "This is a realistic deal, in exceptional circumstances, securing a strong independent BBC for the next six years.
"It means that efficiency and reform will continue to be key issues for us. But our focus remains providing distinctive, high quality programmes valued by the public. This deal will safeguard that until 2017."
BBC Trust chairman Michael Lyons said: "The BBC is not government funded, but these are pressing times for the nation as a whole and we believe licence fee payers would expect us to see what contribution we can properly make."
The BBC's extra responsibilities were "consistent with this and will deliver benefits to licence fee payers across the UK", he added.
Writing on his blog after the deal had been announced, Culture Secretary Jeremy Hunt said: "Sorting out DCMS's budget settlement was an extraordinarily gruelling process, all the more so because we ended up negotiating the BBC's next licence fee settlement as part of it.
"In the end the deal we got was tough but fair. Tough because the BBC, like everyone, is going to have to make demanding efficiency savings.
"But fair because it allows them to continue to make the great programmes that we all love, and licence fee payers won't have to pay any extra for the privilege."
In an e-mail to its members at the BBC, the National Union of Journalists said the deal was "a watershed moment" for the corporation.
"It is our view that the BBC should have fought these plans, and rallied its supporters, rather than accept such a devastating deal which could lead to thousands of job losses and the wholesale closure of services," it said.
The deal appeared to have been "struck at the 11th hour with no consultation with listeners, viewers or staff", it added.
Gerry Morrissey, general secretary of broadcasting union Bectu, accused the BBC of "doing the government's dirty work".
"How can you cut 16% off your costs without affecting jobs or services?" he said.
"Morale at the BBC is already at rock bottom, but now there is little or no confidence in the management."
Meanwhile, shadow foreign secretary Yvette Cooper has warned that "jettisoning" the World Service from the Foreign Office "at this late stage, without serious consultation or a strategy for its future, is cavalier and short-termist".
"Although editorially independent, the World Service is a key component of UK diplomacy and does important work promoting British values and open debate across the world," she said.
It has also been announced that money the BBC had ringfenced to pay for the switchover to digital TV - about £150m a year - will now contribute to the broadband rollout.
The BBC Trust earlier warned the government it would fight any plans to force the corporation to meet the cost of free television licences for the over-75s.