The 56-year-old right-winger will replace Patrick McLoughlin, who could move to another Cabinet role.
Mr Mitchell, a former merchant banker, represents Sutton Coldfield near Birmingham and was the campaign manager for David Davis, the Prime Minister's rival for the Tory leadership in 2005.
His promotion to Chief Whip will place him firmly within Mr Cameron's inner circle.
Mr Mitchell is one of the architects of the Coalition's contentious pledge to increase foreign aid spending to 0.7% of GDP as part of the strategy to detoxify the Tories' "nasty party" image.
"Andrew has done a superb job as Britain's Development Secretary. He has made British development policy transparent, focused and highly effective," the Prime Minister said last night.
"His energy and passionate commitment have placed Britain at the forefront of international efforts to improve the lives of millions of the world's poorest people. He has made a real difference."
He added: "As Chief Whip, Andrew will ensure strong support for our radical legislative programme by working hard to win the argument in the Commons as well as playing a big role in the No 10 team."
In response, Mr Mitchell said: "It has been a huge privilege to serve as part of a Coalition which has radically overhauled the way aid is spent and brought a new rigour to British development policy.
"I am incredibly proud to be part of a government which is improving the lives of the world's most vulnerable people and helping the poorest countries stand on their own two feet."
Sources suggested the "Quad" – the PM, his deputy Nick Clegg, Chancellor George Osborne and his deputy Danny Alexander – met yesterday to hammer out details of the final list of who is up, who is down and who is out.
The complicating factor for Mr Cameron is that the Government is made up of two distinct parties and so, making changes while maintaining the delicate Coalition's equilibrium makes matters even more difficult. One insider has branded the process "three-dimensional chess".
A return of Liberal Democrat David Laws, who just weeks into the Coalition had to resign over an expenses scandal, is expected to happen with a possible move to the Cabinet Office.
The Conservative price is likely to be the promotion of some Tory right-wingers, including Mr Mitchell.
Maria Miller, the Minister for the Disabled, who attracted criticism for the shake-up in Remploy, is expected to replace Cheryl Gillan as Welsh Secretary.
Speculation Ms Gillan was being dropped grew last night when it emerged her Twitter biography had been changed, removing a reference to her being Secretary of State for Wales.
Other hot tips include swapping two Conservative co-chairmen, Baroness Warsi and Lord Feldman, with a single chairman, Grant Shapps, the telegenic Housing Minister. Baroness Warsi, who has made public her desire to stay as co-chairman, could move to International Development. Friends of hers have suggested she was badly bruised by her brush with the authorities – and the media – over allegations she misclaimed expenses. She was later exonerated.
Justine Greening, the Transport Secretary, who has campaigned vigorously against a third runway at Heathrow – her constituency is under the flight path – could be shifted sideways as it looks increasingly likely the Tories could change tack and come out in favour of a third runway.
There could also be changes for Jeremy Hunt at Culture and Andrew Lansley at Health. Chris Grayling, the Employment Minister, is thought to be in line for promotion.
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