Former Education Secretary Michael Gove has been handed "one of the most important jobs" in government, David Cameron has insisted.
Mr Gove has been made chief whip - in charge of party discipline - in the biggest ministerial shake-up of Mr Cameron's premiership.
He was replaced at education by former Treasury Minister Nicky Morgan, as the PM promotes more women into top jobs.
No 10 said it was "quite wrong" to call it a demotion for Mr Gove.
William Hague has stepped down as foreign secretary to be replaced by Philip Hammond in a day of dramatic ministerial movements across government.
With just a handful of junior roles still to be confirmed, Mr Cameron said he was proud to lead "a fresh team with the idea, the energy and the ability to take this country forward".
Asked if the change represented a "punishment" for Mr Gove's recent spat with Home Secretary Theresa May, Mr Cameron said: "I can tell you, if you are prime minister, the chief whip is one of the most important jobs in government.
"I wanted one of my big hitters, one of my real stars, one of my great brains, someone who has done extraordinary things for education in this country, to do that job, to deliver the government's programme, to help secure the future for our country.
"I am pleased that he is doing that job. He will do it brilliantly."
Mr Gove also sought to play down any suggestion that he had been demoted, saying he had worked out the details of his new role - which unlike previous chief whips will see him taking to the airwaves to make the government's case - with the prime minister.
He said it was a "wrench" to leave the education department but whether you called it "demotion, emotion, locomotion" it was "exciting to be given a role at the heart of government".
Among the other changes announced:
- Lord Hill, Leader of the House of Lords, has been nominated as the UK's next European Commissioner
- Liz Truss, a 38-year-old education minister, who entered the Commons in 2010, has been drafted into the cabinet as environment secretary
- Business minister Michael Fallon - a veteran frontbencher - is named as the new defence secretary
- Sir Bob Kerslake is to step down as head of the civil service in the autumn
- Sir Jeremy Heywood, the cabinet secretary, will also be head of the civil service
- David Jones is sacked as Welsh secretary to be replaced by his deputy Stephen Crabb
- David Willetts replaced as universities minister by Greg Clark
- Justice Minister Jeremy Wright, a 41-year-old barrister, replaces Dominic Grieve as Attorney General, the government's chief legal officer
- Baroness Tina Stowell, a former head of corporate affairs at the BBC, is the new leader of the House of Lords
- Mark Harper who quit as immigration minister after admitting employing an illegal immigrant as a cleaner, returns as a work and pensions minister, and Nick Gibb - sacked in a 2012 reshuffle - returns to the education department
The BBC News channel's chief political correspondent Norman Smith said the aim of the reshuffle was to bring in fresh faces and make voters think again about the Conservatives' "male, pale and stale" image.
The number of women in cabinet has gone up from three to five, out of a total of 22 ministers in Mr Cameron's top team. Ten women have been promoted so far, across government, with three taking ministerial jobs for the first time.
But Nick Robinson said it was not the "ideal signal to send" that new Lords leader Baroness Stowell, as a minister who merely "attends cabinet", was to have been paid less than her male predecessor Lord Hill of Oareford, who was a full cabinet member.
After this detail emerged, the Conservatives said they would top up her salary out of party funds to make up the shortfall.
Former Defence Secretary Liam Fox has turned down David Cameron's offer of a return to government as a minister in the Foreign Office, saying on his website he preferred to carry on campaigning on immigration and Europe from the backbenches.
But it is Mr Gove's move to chief whip, announced by Mr Cameron on his Twitter feed, that has caused the most surprise.
Mr Gove has been one of the most radical and at times controversial figures in David Cameron's government, driving through far-reaching changes to the education system such as free schools, exam changes and the extension of the academy programme.
His calls for a return to more traditional teaching methods and exam reforms have brought him into conflict with the unions. His replacement by the relatively unknown Nicky Morgan - seen as having a less confrontational style - may be an attempt to calm things down, said the BBC's Norman Smith.
Downing Street is talking up Mr Gove's new role, which will see him leading the fight against Labour in the general election campaign.
"You should expect to see a great deal of Michael Gove on your TV and radio channels," said the prime minister's official spokesman.
But BBC political editor Nick Robinson said it will be seen by some as a demotion as Mr Gove will no longer be a full cabinet member, just have the right to attend meetings when required.
"He now continues not as a leading Tory figure in his own right but as 'a friend of David and George'," said Nick Robinson.
"His first job would appear to be to help them win the election. His second to make sure Boris and his old sparring partner Theresa May aren't the next Tory leader."
'Surprised and shocked'
Nicky Morgan will add responsibility for equalities to her previous brief as minister for women, but business and education minister Nick Boles will be responsible for implementing same sex marriage legislation, which Mrs Morgan voted against on the basis of her Christianity.
The teaching unions have said they are seeking urgent meetings with Nicky Morgan to discuss pay, pensions and professional standards.
Ofsted chief Sir Michael Wilshaw said he was "surprised and shocked" by Mr Gove's departure, telling LBC radio: "I'm a great admirer of the Secretary of State, I think he's been a transformative and radical minister of education."
By BBC Political Correspondent Robin Brant
Three things to take from this reshuffle:
1. This is about presentation. Unashamedly the prime minister is changing what his government looks and sounds like to voters. It looks like he's doubling the number of women cabinet ministers, albeit from a low starting point of just three. The new education secretary, Nicky Morgan, is a marathon-running working mum. The new environment secretary, Liz Truss, is still in her thirties. But the risk is that some, both inside and outside politics, will see it as just that; presentation, and nothing more.
2. The Tory take on Europe is a key theme to the reshuffle. Arch-Eurosceptic Owen Patterson is out, as are the more Europhile Ken Clarke and the now ex-Attorney General Dominic Grieve. Some in the Conservative Party believe Mr Hague "went native" in his time at the Foreign Office and his anti-Brussels sentiment waned. Much is pinned on the ascension of Phillip Hammond to foreign secretary - he has said the UK should leave the EU if it doesn't get the reforms it wants.
3. The prime minister has gone on to full election fighting mode. Michael Gove and Mr Hague both have less significant jobs but Downing Street is making it clear both will have big campaigning roles. The respected statesman from the north and the uber-polite, articulate - although his toxicity became too much at education - son of adoptive parents will be prominent media performers between now and May 2015.
Other women to be promoted into ministerial roles, outside of the cabinet, include Anna Soubry, who becomes a defence minister, Clare Perry, who goes to transport, and Priti Patel, who becomes Exchequer Secretary at the Treasury.
Environment Secretary Owen Paterson has effectively been fired, while former Commons leader Andrew Lansley has also left the government - and announced his intention to leave Parliament at the 2015 general election.
Mr Lansley's resignation letter suggested he had Mr Cameron's support to take on a "role in international public service in the months ahead" - but did not give further details.
The biggest name in the changes was Mr Hague, who announced late on Monday that he had decided to step down as an MP at next year's general election after 26 years - including four turbulent years as Tory leader.
Until then he will be, as Mr Cameron put it, his "de facto political deputy" and leader of the House of Commons. Mr Hague said he was "delighted" with his new role as he had always enjoyed speaking in the Commons and explained his retirement at the next election by saying he wanted to return to his successful writing career and to spend more time with his wife.
'Massacre of moderates'
Some see the appointment of Mr Hammond, who has said he could vote to leave the EU if the UK did not get the changes it wanted in a future re-negotiation, and the departure of Dominic Grieve - who would oppose any attempt to take Britain out of the European Convention on Human Rights - as a shift towards a more Eurosceptic stance.
But Ken Clarke - the cabinet's most prominent Europhile - heading for ministerial retirement after a career in frontline politics that stretches back to the early 1970s - dismissed such claims, telling BBC Radio 4's Today programme: "If the whole thing is all about Europe then we really have gone mad."
He also praised Mr Cameron's decision to promote more women into frontline roles, saying it was long overdue.
Labour has described the reshuffle as the "massacre of the moderates", claiming it marks a lurch to the right on Europe and a range of other issues.
The party also poured scorn on claims more women were being promoted, saying "half the new faces in the cabinet we've heard of so far are male".
Labour's Shadow Minister for Women and Equalities Gloria De Piero said: "The Tories have spent the last few days briefing that this would be the reshuffle which fixed David Cameron's 'women problem' but it's turning in to a damp squib."
Among other changes:
- Esther McVey - who was tipped for promotion - will remain as employment minister but with the added status of attending cabinet meetings
- Matt Hancock is given a minor promotion at the business department and will attend cabinet
- A cull of long-serving ministers includes chief whip Sir George Young, minister for civil society Nick Hurd, Foreign Office minister Hugh Robertson, energy minister Greg Barker, international development minister Alan Duncan, Northern Ireland minister and policing minister Damian Green