In keeping with the tradition Cameron was invited by Queen Elizabeth II to form the new government shortly before 8.30pm.
Cameron, who became the youngest Prime Minister since 200 years, was greeted with cheers as he drove to 10 Downing Street, London, to make his Prime Ministerial speech.
"This is going to be hard and difficult work," he was quoted in a media reports, adding that coalition government "will throw up all sorts of challenges. But together, I believe we can provide the strong and stable government this country needs."
"Nick Clegg and I are both political leaders who want to put aside party differences and work hard for the common good and for the national interest," Cameron said.
Liberal Democrat leader Nick Clegg would assume office as the Deputy Prime Minister.
US President Barack Obama telephoned Cameron to congratulate him on the occassion