the Conservatives back into power after 13 years.
Mr Cameron, 43, is in Downing Street after traveling to Buckingham Palace to formally accept the Queen's request to form the next government.
He said he aimed to form a "proper and full coalition" with the Lib Dems to provide "strong, stable government".
His party won the most seats in the UK general election last week, but not an overall majority.
In a speech at Downing Street, Mr Cameron said he and Lib Dem leader Nick Clegg would "put aside party differences and work hard for the common good and the national interest".