"We believe the offer represents good value for Cadbury shareholders... and will now work with the Kraft Foods' management to ensure the continued success and growth of the business," said Cadbury's chairman Roger Carr.
Irene Rosenfeld, the chairman and chief executive of Kraft Foods, said the deal was good news for shareholders and staff.
"We have great respect for Cadbury's brands, heritage and people," she said. "We believe they will thrive as part of Kraft Foods."
The deal is a significant increase on earlier Kraft bids, which were flatly rejected by the Cadbury board as "derisory".
Kraft's previous offer valued the company at £10.5bn - a bid Cadbury's chairman Roger Carr said was an attempt to "buy Cadbury on the cheap".
Shareholders are expected to agree to the takeover.
David Cumming, head of UK equities at Cadbury shareholder Standard Life, said that he would be agreeing, despite hoping for a higher price.
John Cadbury, a Quaker, opened a shop in Birmingham in 1824, selling tea, coffee and hot chocolate - as an alternative to alcohol
Dairy Milk brand introduced in 1905, with Milk Tray coming 10 years later
Merged with rival confectioner J.S. Fry & Sons in 1919
Merged with Schweppes drinks business in 1969. Its drinks arm was spun off in 2008
"I won't go against the view of Cadbury's management," he told the BBC.
"Kraft are getting a good deal. It's sad that Cadbury is gone, but business is business."
In early trading on Tuesday, Cadbury shares were up 3.5%.
Unions have expressed concerns that the Kraft takeover could cost jobs.
The company has given no specific assurances over the future of 4,500 UK jobs, though it says it wants to invest in the Bournville site and maintain production at Somerdale, near Bristol, also known as Keynsham.
It has not ruled out cuts, and staff numbers at Cadbury's head office in Uxbridge are expected to be reduced, according to the BBC's business editor Robert Peston.
Founded in Illinois as a cheese wholesaler in 1903
Bought in 1988 by Philip Morris, which also purchased Nabisco for $19.2bn in 2000 before integrating it into Kraft Foods
More than 40 of its brands are more than 100 years old
Has 98,000 employees and 168 manufacturing and processing facilities worldwide
Kraft brands include: Kenco, Ritz, Philadelphia spread, Tang, Alpen Gold and Oreo
Kraft also said it expected "meaningful cost savings" as a result of the merger.
Jennie Formby from the Unite union said the need for Kraft to cut costs could mean staff cuts in the longer-term.
"We are concerned about the levels of debt that Kraft has," she told the BBC.
"The sad truth is that when they have to pay down that debt, the soft option is jobs and conditions.
"When you have to make cost savings of the magnitude they will need to make, you have to ask where those cost savings will be made."
Those fears were shared by David Bailey, professor at Coventry University Business School.
"Serious questions need to be asked about Kraft's intentions," he said.
"Kraft already has a track record of cutting production and moving production abroad. There's no guarantee that they'll keep production in the UK in the long run."
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