He thanked his "amazing " wife, Samantha, who was watching from the public gallery with their three children. "But I do believe that today our country is much stronger", he said, surrounded by his wife and children.
Theresa May 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.
Reacting to Mrs May taking office, Labour leader Jeremy Corbyn said: "I welcome Theresa May's acknowledgement that, after six years of Tory government in which she was a senior minister, the economy is not working for working people".
London, David Cameron has formally resigned as British Prime Minister to pave way for his successor, Home Secretary Theresa May, Buckingham Palace confirmed in a statement on Wednesday.
After the remarks, May stopped and waved outside No. 10 Downing Street beside her husband, Philip.
Before Mrs May's visit to Buckingham Palace, the Queen accepted Mr Cameron's resignation as prime minister.
May, the second female prime minister after Margaret Thatcher, has repeatedly said that "Brexit means Brexit".
"This is a clear indication not only of your determination to use high political office for the protection of some of the world's most vulnerable people but also of your willingness to work with the Catholic Church at its highest levels", the cardinal said in the letter, released to the media July 12. After all, as I once said: ""I was the future once"," said Cameron, who has said he intends to carry on as a backbench Conservative party MP for Witney in Oxfordshire.
She also stood firm on her promise that Brexit means Brexit.
Theresa May's new cabinet is already starting to take shape, with Reuters reporting the resignation of finance minister George Osborne.
Mr Corbyn insisted there will be "plenty more to come" for Mrs May after telling MPs he has asked Mr Cameron 179 questions.
"The government I lead will not be driven by the interests of the privileged few, but by yours".
She is expected to announce the make up of her new cabinet later, with the the key roles of chancellor, home secretary and foreign secretary set to be filled first. "I appreciate the maturity of judgment, the steely resolve, the sense of justice and the personal integrity and warmth you have always shown".
Mrs May was appointed the UK's second female prime minister in a private audience with the Queen at which she was invited to form a government.
"Following the referendum, we face a time of great national change and I know because we are Great Britain, we will rise to the challenge", May said outside the prime minister's Downing Street office.
The procession comes after Cameron fell short of leading the country away from its decision to leave the European Union (EU) in last month's referendum.
Speaking outside 10 Downing Street in her first speech as PM, she said: "Together we will build a better Britain".
Before his 180th question, Mr Corbyn wished Mr Cameron and his family well.