Video: Cameron takes rightful prize as Tories cut historic deal with Lib Dems

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Following his triumphant arrival last night at No 10, the new Conservative Prime Minister declared that it would be a "full and proper" coalition between the two parties.

No 10 confirmed that Nick Clegg had been appointed Deputy Prime Minister, serving as one of five Lib Dem ministers in the new administration.

They are thought to include his chief of staff Danny Alexander, who was being tipped for Scottish Secretary, and children's spokesman David Laws - both members of the Lib Dem team which negotiated the coalition deal with the Tories.

Other posts confirmed last night were George Osborne as Chancellor and William Hague as Foreign Secretary. Liam Fox as Defence Secretary and Andrew Lansley as Health Secretary were also thought to have retained their shadow cabinet portfolios.

On the Lib Dem side it is thought that there will be Cabinet jobs for treasury spokesman Vince Cable and home affairs spokesman Chris Huhne, as well as a number of junior postings.

The appointment of so many Lib Dem ministers means that a number of Tory shadow ministers will be out of luck and one of Mr Cameron's first tasks may be to placate those who are among the disappointed.

Following a late-night meeting of Lib Dem MPs and the party's federal executive to endorse the deal, Mr Clegg sought to reassure his supporters in the country who were unhappy at the idea of a coalition with the Conservatives.

"I can imagine this evening you will be having many questions, maybe many doubts, about this new governing arrangement," he said.

"But I want to assure you that I wouldn't have entered into this agreement unless I was genuinely convinced that it offers a unique opportunity to deliver the kind of changes you and I believe in."

Details of the power-sharing agreement hammered out over five days of negotiations began to emerge in last night in Westminster briefings.

Under the terms of the deal the UK will move to five-year fixed-term parliaments with the next election to be called on the first Thursday of May 2015.

On the central issue of reducing Britain's record 163 billion deficit, they will go ahead with the Tories proposed 6 billion of spending cuts this year.

The will also scrap the bulk of the planned increase in national insurance contributions for employers.

But instead of getting rid of the rise for employees, there will be a "substantial increase" in personal tax allowances to benefit low and middle-income workers, as the Lib Dems had been calling for.

The Lib Dem manifesto pledge to take everyone earning under 10,000 out of income tax altogether will be a long-term goal with "real terms steps" being taken each year, although with no timetable set for its achievement.

The Lib Dems have also won a referendum on changing the Westminster voting system - from first-past-the-post to the additional vote rather than the full proportional representation they had wanted.

The Conservatives accepted that their plans to exempt estates worth up to 1 million from inheritance tax were unlikely to be implemented - while Lib Dem promises of a "mansion tax" on 2 million-plus properties will also be abandoned.

The Lib Dems will not be required to support proposals for a tax break for married couples - although the Tories remain hopeful it would be approved.

But they will sign up to a commitment not to join the European single currency and to legislation requiring a referendum on any proposed transfer of powers to the European Union.

And the Conservatives will retain their promise of a cap on immigration and implement in full their welfare reform and school reform programmes.

In another area of significant disagreement - Trident nuclear missiles - the new joint administration will be committed to "the maintenance of Britain's nuclear deterrent".

But the Liberal Democrats will be allowed to "continue to make the case for alternatives" and insist that the renewal of Trident be scrutinised to ensure it offers value for money.

Nuclear power is another of several issues where different positions will be allowed.

There was agreement on a series of civil liberties-related policies, such as scrapping the ID card programme and its national register and the next generation of biometric passports, reviewing libel laws and further regulation of CCTV cameras.

There was also agreement on imposing a levy on banks and tackling excessive City bonuses but a independent commission will be set up to decide which party's different visions of how to split up the banking sector should be implemented.

Gordon Brown, whose dramatic resignation last night paved the way for the new government, was back home in Scotland today with his wife Sarah and their two children.

It is thought that he will now stand down as an MP and quit politics altogether - friends said that they expected him to concentrate on charity work.

The Prime Minister left his west London home at 7.40am today.

Wearing a dark suit, he said 'good morning' to reporters but did not take any questions.

He was then driven away in an official Government Jaguar.

Appearing on GMTV, Mr Laws and Mr Gove claimed the coalition would be popular with the public.

Mr Gove said: "I think the fact that you have got two parties that are prepared to work hard to agree and to form a government in the national interest, I think that people in the shires and in our cities across the country will actually be pleased and relieved that a new style of politics has meant that you can have people from different parties, different traditions, working together in the national interest."

Mr Laws denied that the Liberal Democrats had "sold their soul" to join the coalition.

He said: "Of course, in these agreements, there is a degree of compromise, but I think that when you see the agreement and when you compare that with the key parts of the Liberal Democrat manifesto, that people who voted Liberal Democrat will be very pleased.

"I am also actually very proud, stepping back and viewing this as a citizen, I think most people in this country, regardless of which party they voted for, will think that there is a lot good in this document."

Journalists greeted the new Prime Minister and asked him how he was feeling, but as he walked into Number 10, he just smiled and gave a small wave.

The Deputy Prime Minister left his south west London home at 8.20am today.

He smiled and greeted waiting reporters but declined to answer any questions before being driven to Downing Street in an official Government Jaguar.

Mr Hague arrived at Downing Street at 8.35am.

He told BBC Radio 4's Today programme that the Tory/Lib Dem coalition represented a "realignment" of British politics.

He revealed that a document setting out the terms of the coalition, being published later today, would name areas - including the married tax allowance, nuclear power and university funding - where Liberal Democrats will be allowed to abstain from Government measures.

Mr Hague said he hoped there would not be any "difficulties" over the issue of the European Union.

"We have written into this agreement that we agree there should be no further transfer of sovereignty or powers over the course of the next Parliament, and that was not a difficult item to agree with the Liberal Democrats."

But he said on the broad range of policy, the parties had been able to agree a platform which both could push forward.

Mr Hague confirmed that the new Government intends to introduce fixed-term Parliaments, with the next election to be held on the first Thursday of May 2015.

And he confirmed that former News of the World editor Andy Coulson will head the media operation of the coalition government, which he said would avoid the "spin" of the New Labour years.

"This Government will be judged by whether it really brings down the deficit, reforms taxes so there is a fairer tax system, and improves the education system, not by whether it reannounces and misannounces and falsely announces a whole string of things every day, which was the style of the Blair and Brown years," said Mr Hague. "We are determined to change that."

Mr Hague said that Britain's first coalition for 70 years would require some "innovations" in the way Government operates.

"There are one or two measures on which we have agreed, since the parties have very different policies, that the Government will be able to bring forward measures and the Liberal Democrats will be able to abstain - for instance on the married tax allowance," he said, adding that this would also apply to higher education funding and nuclear power.

"Across the whole programme of deficit reduction, tax reform - with the exception of married tax allowance - immigration, major political reforms and constitutional change, on pensions and welfare, on the rest of education policy, civil liberties and the environment, we have reached true collective agreement."

Mr Hague acknowledged that there would be some people on both sides who would find the arrangement difficult to accept.

"This is a genuine compromise between the parties," he said. "There are many things the Liberal Democrats have had to swallow that are very difficult for them, just as there are some things - like holding a referendum on a new voting system - that are very difficult for the Conservative Party to accept.

"That means, of course, there will be people in both parties who quietly wish it hadn't happened, I'm sure.

"But the acclamation for this agreement amongst both parties was very, very strong last night and I think if we can show we can continue to work in this way, then any little resentments will be put into perspective."

Mr Hague said Mr Cameron and Mr Clegg had already shown during the negotiations over a coalition that they had a "very good working relationship".

"One of the most striking things in the negotiations was not just that we reached agreement, but the manner in which we reached agreement," he said. "We found an excellent working relationship between the parties."

He accepted there would inevitably be disputes between the different sides of the new Government.

"Of course that will happen," said Mr Hague. "The way to resolve disputes is through the relationship between the Prime Minister and Deputy Prime Minister and having seen them work together and talk together over the last few days, if we can resolve this situation - a hung Parliament where we have been campaigning against each other - their ability to resolve this situation bodes very well for our ability to make this work in government."

Next page: David Cameron's speech in full This is the text of Mr Cameron's remarks in Downing Street:

"Her Majesty the Queen has asked me to form a new government and I have accepted.

"Before I talk about that new government, let me say something about the one that has just passed.

"Compared with a decade ago, this country is more open at home and more compassionate abroad and that is something we should all be grateful for and on behalf of the whole country I'd like to pay tribute to the outgoing prime minister for his long record of dedicated public service.

"In terms of the future, our country has a hung parliament where no party has an overall majority and we have some deep and pressing problems - a huge deficit, deep social problems, a political system in need of reform.

"For those reasons I aim to form a proper and full coalition between the Conservatives and the Liberal Democrats.

"I believe that is the right way to provide this country with the strong, the stable, the good and decent government that I think we need so badly.

"Nick Clegg and I are both political leaders that want to put aside party differences and work hard for the common good and for the national interest.

"I believe that is the best way to get the strong government that we need, decisive government that we need today.

"I came into politics because I love this country. I think its best days still lie ahead and I believe deeply in public service.

"And I think the service our country needs right now is to face up to our really big challenges, to confront our problems, to take difficult decisions, to lead people through those difficult decisions, so that together we can reach better times ahead.

"One of the tasks that we clearly have is to rebuild trust in our political system. Yes that's about cleaning up expenses, yes that is about reforming parliament, and yes it is about making sure people are in control - and that the politicians are always their servant and never their masters.

"But I believe it is also something else. It is about being honest about what government can achieve. Real change is not what government can do on its own - real change is when everyone pulls together, comes together, works together, where we all exercise our responsibilities to ourselves, to our families, to our communities and to others.