Mr Cameron handed his resignation during a visit to Buckingham Palace, shortly after addressing a crowd outside No. 10 Downing Street.
The Queen has subsequently invited Mrs Theresa May to form a new government.
The former home secretary travelled to Buckingham Palace where she officially accepted the Queen’s invitation to form a new government.
She becomes the UK’s second ever female PM, after Margaret Thatcher.
Mrs May, who at 59 becomes the oldest incoming prime minister since Jim Callaghan in 1976, will then return to No 10 as the country’s second female prime minister, following in the footsteps of Margaret Thatcher.
She is expected to briefly address the nation before meeting top officials, including Cabinet Secretary Sir Jeremy Heyward, and receiving a full national security and defence briefing.
She will be asked to hand-write letters to the commanders of the UK’s four Trident submarines about what to do in the event of a catastrophic nuclear attack on the UK and to appoint two nuclear “deputies” – ministers who will take decisions on the deterrent if she has been rendered incapable.