A seismic shift in politics as Cameron and Clegg launch historic double act - VIDEO

In their first public appearance together since agreeing the deal on Tuesday night, the pair lapped up the sunshine in Downing Street's Rose Garden in a remarkable display of warmth from two men who only days before had been at loggerheads on the campaign trail.

Mr Cameron insisted the new deal offered real hope of a bright future and confessed he had found the idea of leading a minority government "uninspiring" after becoming the first Prime Minister to lead a coalition government since the Second World War.

Mr Clegg, who will take personal charge of driving through political reform in his role as Deputy Prime Minister, was adamant the agreement would last despite the inevitability of "bumps and scrapes" as he admitted: "Until today, we have been rivals, now we are colleagues."

Yesterday Mr Cameron began putting together his government by installing his Cabinet – including five seats for the Lib Dems – with Theresa May the most surprising appointment as Home Secretary.

Richmond MP William Hague was confirmed as Foreign Secretary and George Osborne as Chancellor, while Vince Cable becomes Business Secretary and David Laws Chief Secretary of the Treasury for the Lib Dems.

Former Tory leader Iain Duncan Smith is Work and Pensions Secretary, Ken Clarke will be Justice Secretary, Dewsbury peer Sayeeda Warsi becomes the first female Muslim Cabinet Minister as Tory party chairman and former Bradford Council leader Eric Pickles is the new Communities and Local Government Secretary.

Former Shadow Transport Minister Robert Goodwill, Tory MP for Scarborough and Whitby, and Greg Mulholland, Lib Dem MP for Leeds North West, will be among those waiting for the phone to ring today as lower ranking Ministerial posts are handed out.

On their first full day in power – after four days of painstaking negotiations that had threatened to break down until Gordon Brown was forced to admit defeat and resign – the two parties published details of their deal which revealed the Tories were forced to abandon plans to scrap next year's National Insurance increase for employees as well as delaying any inheritance tax cuts and raising capital gains tax, hitting second homes, buy-to-lets and shares.

But an emergency Budget due within 50 days will increase the income tax threshold "substantially" from next April to negate the impact of the National Insurance increase. The NI increase for employers will still be scaled back to boost jobs.

The Queen's Speech on May 25 is also expected to include legislation to introduce fixed-term parliaments which will mean the Cameron-Clegg coalition stays in power until May 2015.

On his first full day in power, one of Mr Cameron's first acts was to establish a National Security Council – headed by top Foreign Office civil servant Sir Peter Ricketts and including Mr Clegg and several senior Ministers. It met for the first time last night to discuss the situation in Afghanistan and Pakistan and review the terrorist threat to the UK.

Mr Clegg, MP for Sheffield Hallam, fills the role of Deputy Prime Minister left empty since another Yorkshire MP, John Prescott, quit with Tony Blair nearly three years ago.

He said both he and Mr Cameron had taken "big risks" in joining forces and vowed: "We will now have to show the sceptics who predict that it will go wrong that they are wrong."

He added: "This is a new government, and it's a new kind of government, a radical, reforming government where it needs to be and a source of reassurance and stability at a time of great uncertainty in our country too."

Meanwhile, in the ranks of the Opposition and while the nation's focus was on the beginnings of the new coalition, former Foreign Secretary David Miliband became the first Labour MP to announce he would stand in the party's contest to become leader.

Alan Johnson, former Home Secretary and MP for Hull West and Hessle, said he would back Mr Miliband after announcing he would not be standing himself.