The decision to move the former international development secretary, who once served as a UN peacekeeper, is an attempt to instil discipline into the parliamentary Conservative party.
Mitchell will replace Patrick McLoughlin, who is set to stay in the government. Last night multiple reports suggested that McLoughlin could replace Justine Greening as transport secretary.
But Cameron has limited room for manoeuvre because most leading members of the cabinet, including chancellor George Osborne, foreign secretary William Hague, home secretary Theresa May and business secretary Vince Cable, are set to retain their positions.
Welsh secretary Cheryl Gillan did not confirm that she has left the cabinet but has removed all mention to her ministerial role from her biography on Twitter.
Full details of the reshuffle are expected today, including a likely return to government for leading Liberal Democrat David Laws.
Meanwhile Deputy Prime Minister Nick Clegg yesterday told the Commons that the government has officially withdrawn plans to reform the House of Lords following a successful protest by backbench Conservative MPs.
Clegg also confirmed that in retaliation the Lib Dems would vote against forthcoming reforms to constituency boundaries, although the government still intends to push ahead with a vote on the issue next year.