The announcement comes in that aftermath of the EU Referendum result
David Cameron has resigned as Prime Minister after the UK public voted to leave the European Union in the referendum.
A tearful Cameron, with his wife by his side, said he had already spoken to the Queen about his decision.
The Prime Minister campaigned to remain in the EU, but the 'Out' campaign won by 51.9% to 48.1% as over one million more people voted to Leave.
Speaking to masses of reporters outside Downing Street, Cameron said that there was no precise timeline for his departure.
He said he would like to see a new leader to be in place by the Tory party conference in October, but will continue to carry out his duties until then.
"The British people have voted to leave the European Union and their will must be respected," Mr Cameron said.
He called it "an instruction that must be delivered" as he also thanked his supporters and congratulated Leave campaigners for their "spirited and passionate case".
The Prime Minister said he had fought "head, heart and soul" to stay in the union but that the British people had chosen a different path.
Earlier, UKIP leader Nigel Farage said a "dawn is breaking on an independent United Kingdom", and called for the Prime Minister to step down.