Before Mrs May's visit to Buckingham Palace, the Queen accepted Mr Cameron's resignation as prime minister.
Theresa May today became Britain's second woman prime minister after Margaret Thatcher, vowing to forge "a bold new positive role" for the United Kingdom in the world post-Brexit.
One of May's first tasks will be to select her Cabinet.
In her first appointment after taking office, May named former foreign secretary Philip Hammond as Britain's finance minister. Osborne has resigned from government.
She added: "We will forge a bright, new, positive role for ourselves in the world".
Michael Fallon has kept his job at the Ministry of Defence - a position he has held since 2014.
Speaking to the world's press outside Number 10, she said the decisions of her administration would be driven not by the interests of "the privileged few" but those voters struggling with the pressures of modern life.
After the short meeting, Mrs May travelled by auto to Downing Street where she made her first speech as PM, telling crowds of reporters and photographers she would build a country that works not just for the "privileged few".
Mrs May inherits a government transformed in less than a month by the referendum vote for Britain to leave the European Union which lead to her predecessor David Cameron resigning as leader. "Together we will build a better Britain".
He thanked his "amazing " wife, Samantha, who was watching from the public gallery with their three children.
Mr Cameron concluded: "It has been the greatest honour of my life to serve our country as Prime Minister over these last six years and to serve as leader of my party over 11 years".
May assumed office after meeting with Queen Elizabeth and drove straight to her new home of 10 Downing Street, vacated hours earlier by David Cameron.
David Cameron recalled the time his youngest daughter Florence climbed into one of his red ministerial boxes just before a foreign trip and pleaded to be taken with him.
Earlier in the day, Cameron made his final appearance in the House of Commons, where he received a standing ovation for his performance after six years in the job. "I will miss the roar of the crowd, I will miss the barbs of the opposition, but I will be willing you on".
"The full title of my party is the Conservative and Unionist Party, and that word unionist is very important to me", May said.
Cameron had campaigned hard for Britain to stay within the European Union, but Britons voted by 52 percent to leave on June 23, plunging the country into uncertainty. Others possibly in line for promotion to the Cabinet include the Works and Pensions minister Priti Patel, who played a prominent role in the Brexit campaign, and the Business minister, Anna Soubry, who backed Remain.
During his last audience with the Queen, Mr Cameron tendered his resignation as Prime Minister.