Andrew Lansley has been replaced as Health Secretary by Jeremy Hunt as part of an extensive government reshuffle.
The move is a promotion for Mr Hunt, who has been under pressure for his handling of the BSkyB takeover bid.
Elsewhere, Chris Grayling replaces Ken Clarke as Justice Secretary and Transport Secretary Justine Greening is controversially moved to another role.
London Mayor Boris Johnson criticised Miss Greening's move, suggesting it heralded a rethink on aviation policy.
Miss Greening - a strong opponent of a new runway at Heathrow - has been replaced by former Conservative Chief Whip Patrick McLoughlin after less than a year in the job and will take over the lower-profile role as International Development Secretary.
Unlike Miss Greening, Mr McLoughlin - who was a transport minister under Lady Thatcher and Sir John Major - is said to have "no baggage" over Heathrow expansion.
Mr Johnson said the development was a sign the government may rethink its approach to new air capacity in the south of England.
He described her as a "first-rate transport secretary" and said her opposition to Heathrow expansion was the "only possible" reason for the change and promised to fight this all the way.
The reshuffle is the Prime Minister David Cameron's first major restructuring since the Conservative-Lib Dem government came to power in 2010.
The changes have not affected key figures such as Chancellor George Osborne, Home Secretary Theresa May or Foreign Secretary William Hague - who will all remain in their posts.
Education Secretary Michael Gove and Work and Pensions Secretary Iain Duncan Smith will also stay in their jobs, with Downing Street saying it wanted these "strong reformers" to continue their work.
The BBC understands Mr Duncan Smith was offered the job of Justice Secretary but turned it down.
Those leaving the government in the shake-up include Environment Secretary Caroline Spelman, Welsh Secretary Cheryl Gillan and Commons leader Sir George Young.
Among notable promotions, Maria Miller and Theresa Villiers join the cabinet as Culture Secretary and Northern Ireland Secretary and Housing Minister Grant Shapps becomes Tory Party co-chairman.
BBC political editor Nick Robinson said the changes at health, transport and justice were intended to address perceived Conservative weaknesses in the long run-up to an election scheduled for 2015.
Speaking outside No 10, Mr Hunt said he was "incredibly honoured" to take charge of the Department of Health.
"It is a huge task and the biggest privilege of my life," he told the BBC.
Mr Lansley, the architect of controversial reforms to the NHS in England, has effectively been demoted to the more junior role of leader of the House of Commons.
Mr Clarke also takes a lesser role as minister without portfolio in the Cabinet Office, where he will act as a government "wise head" offering advice to Mr Cameron on issues including economic strategy.
He has been replaced by employment minister Chris Grayling, who was shadow home secretary before the 2010 election and is regarded as being to the right of Mr Clarke on justice issues.
Mr Clarke denied the move was a humiliation and he was "pleasantly surprised" to remain in cabinet.
He added: "At my age you do occasionally have to step down from a heavy departmental role before you suddenly realise you can no longer quite handle it."
Among other changes, former Northern Ireland Secretary Owen Paterson becomes the new Environment Secretary, while Wales Office minister David Jones has been promoted to Welsh Secretary.
Baroness Warsi has lost her job as Conservative Party co-chairman but will continue to attend cabinet in the dual role of Foreign Office minister and minister for faith and communities.
Below cabinet level, Solicitor General Edward Garnier, defence minister Gerald Howarth, prisons minister Crispin Blunt and Children's minister Tim Loughton have all been axed, while policing minister Nick Herbert has resigned after reportedly turning down a move to the Department for the Environment, Food and Regional Affairs.
But Paul Deighton, chief executive of the London 2012 organising committee, will be given a peerage and become a Treasury minister. Treasury minister Chloe Smith moves to the Cabinet Office. She is replaced by Sajid Javid.
All five Liberal Democrat cabinet ministers, including Business Secretary Vince Cable, will remain in their posts.
But there are changes lower down the Lib Dem ranks. Former cabinet minister David Laws - who resigned over his expenses in 2010 - has returned to the government as a junior education minister.
He replaces Sarah Teather, who is leaving the government - along with Lib Dem care services minister Paul Burstow and defence minister Nick Harvey.
But there are promotions for Norman Lamb and Jo Swinson, both close to Mr Clegg. Jeremy Browne moves from the Foreign Office to the Home Office.
Pressure has been growing on Mr Cameron in recent months, with several Conservative MPs accusing the coalition of not doing enough to promote economic growth.
In response to Tuesday's changes, backbencher Peter Bone said Mr Cameron seemed to be "listening to his party" and the new team had a more "traditional look".
But Labour said there would be no change in economic policy with George Osborne remaining in place.
"This is the no-change reshuffle," said shadow Cabinet Office minister Michael Dugher.
He added: "This reshuffle isn't a fresh start - it's more of the same from an out-of-touch and failing government that stands up for the wrong people."
Other Conservative appointments so far include:
Hugo Swire - Foreign Office minister
Damian Green - policing minister
Matthew Hancock - business and education minister
Michael Fallon - business minister
Daniel Poulter - health minister
Anna Soubry - health minister
Philip Dunne - defence minister
Helen Grant - justice minister
Jeremy Wright - justice minister
Stephen Hammond - transport minister
John Hayes - education minister
Elizabeth Truss - education minister
Esther McVey - work and pensions minister