Tim Davie, the former BBC director of audio and music and incoming BBC Worldwide chief executive, will be acting director general until a permanent replacement is found.
Entwistle was widely criticised today following an interview on BBC Radio 4 this morning in which he said he had not known about the 'Newsnight' claims until the day after they screened because he was out the evening they were broadcast (2 November).
'Newsnight' was already under pressure after it emerged that an investigation into claims the deceased TV and radio presenter Jimmy Savile was a paedophile was shelved last year shortly before the BBC broadcast a number of Christmas specials about Savile.
This evening Entwistle said in a statement: "As director general of the BBC, I am ultimately responsible for all content as the editor-in-chief, and I have therefore decided that the honourable thing for me to do is to step down."
The chairman of the BBC Trust Lord Pattern said Entwistle has "very honourably offered us his resignation because of the unacceptable mistakes and the unacceptable shoddy journalism which has caused so much controversy".
Full statement from Lord Patten:
"This is undoubtedly one of the saddest evenings of my public life. George Entwistle worked for the BBC for 23 years. He exemplifies the finest values of public service broadcasting. At the heart of the BBC is its role as a trusted global news organisation, and as the editor-in-chief of this organisation, George has very honourably offered us his resignation because of the unacceptable mistakes and the unacceptable shoddy journalism which has caused so much controversy.
"He has behaved as editor with huge honour and courage and would that the rest of the world always behaved the same. George was set on putting in place a number of reforms and changes which will be required in this great organisation and it is a real tragedy that he has been overwhelmed by these events, as we all were to a great extent, before he was able to act in a way that was clearly necessary.
"As from tomorrow, the acting director-general will be Tim Davie and we will begin the process of agreeing on a permanent successor."