History Made as Theresa May Becomes UK's Second Female Prime Minister Ever (Photo)
The former home secretary travelled to Buckingham Palace where she officially accepted the Queen's invitation to form a new government.
In his farewell statement outside Downing Street, Mr Cameron said Mrs May would provide "strong and stable leadership" and wished her well in her negotiations with the EU.
Before Mrs May's visit to Buckingham Palace, the Queen accepted Mr Cameron's resignation as prime minister.
Mrs May, 59, suddenly won the Conservative leadership contest after rival candidate Andrea Leadsom pulled out on Monday.
One of her first tasks will be to appoint her new ministerial team.