She will appoint the first few key members of her Cabinet tonight, with other appointments to follow.
“The Government I lead will be driven not by the interests of the privileged few, but by yours,” she said.
“When we take the big calls, we’ll think not of the powerful, but you, when we pass new laws, we’ll listen not to the mighty, but you, when it comes to new taxes we’ll prioritise not the wealthy, but you.
“As we leave the European Union we will forge a bold new positive world for ourselves, and we will make Britain a country that works for everyone of us.
“That will be the mission of the government I lead, and together we will build a better Britain.”
Cameron leaves Number 10
Ms May, 59, was invited to form a government by Queen Elizabeth II in a private audience at Buckingham Palace after Mr Cameron resigned.
She arrived at the palace by ministerial car with her husband Philip May, having set off from the House of Commons after Mr Cameron was officially accepted by the Queen.
Mr Cameron advised the Queen to appointed the former Home Secretary in his place.
Theresa May in quotes
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A spokesperson for the Palace said: "The Queen received in audience Theresa May and requested her to form a new Administration."
In a brief address outside Downing Street before he resigned, Mr Cameron said: "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.
"And as we leave for the last time, my only wish is continued success for this great country that I love so very much."
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