Cameron, 43, became prime minister when Labor's Gordon Brown stepped down Tuesday. That ended the political deadlock after last Thursday's elections gave Cameron's Conservative Party a plurality, but not majority, of seats in Parliament's House of Commons.
The Conservatives won 306 seats in the 650-seat House of Commons. Brown's Labor Party was next at 258 and the Liberal Democrats third with 57, creating a hung Parliament.
Brown, as sitting prime minister, could have tried to form a government but stepped aside leaving Cameron to turn to the Nick Clegg and the Liberal Democrats to put together a working majority.
The economy will be first order of business for Cameron, who was greeted on his first full day in office with word unemployment in the United Kingdom is at its highest since 1994.
The coalition, the first such ruling agreement in Britain since World War II, is an unexpected mix and as a commentator for American Public Media's Marketplace Morning Report related, "the cynics are saying it may not be too long before the two governing parties are fighting like ferrets in a sack."
Clegg, however, said he doesn't see such conflicts as inevitable.
"I hope this is the start of the new politics I have always believed in -- diverse, plural, where politicians of different persuasions come together, overcome their differences in order to deliver good government for the sake of the whole country," he said, even while admitting his party members have "many questions, maybe many doubts."