Dyke's decision to step down follows BBC chairman Gavyn Davies' resignation on Wednesday, shortly after Lord Hutton's report into events which led to the suicide of weapons expert David Kelly was published.
And British Prime Minister Tony Blair has accepted an unreserved apology from the BBC for errors in a report alleging that his government doctored intelligence on Iraq.
"On behalf of the BBC I have no hesitation in apologising unreservedly for our errors and to the individuals whose reputations were affected by them," the acting chairman of the BBC, Lord Richard Ryder, said in a statement.
Blair meanwhile has said "this for me has always been a very simple matter of an accusation that was a very serious one that was made. It has now been withdrawn, that is all I ever wanted."
A report on the BBC's website states that "the resignations follow former Downing Street media chief Alastair Campbell's claim that Mr Davies and Mr Dyke had made things worse by continuing essentially to stand by the story".
The report adds that the departure of both the BBC chairman and director general "leaves the corporation leaderless at a time when calls have been growing for the BBC to come under outside regulation".
The resignations come as British Prime Minister Tony Blair demanded an apology from the BBC after the Hutton report cleared his government of allegations that it doctored intelligence on Iraq.
"We still do want an apology," Blair's spokesman told reporters.
Culture Secretary Tessa Jowell has said the Hutton report will be taken into account in the 2006 review of the BBC's charter.
In his resignation statement, Davies said that as the man at the top he had to take responsibility, the BBC reported.
The report added that Davies questioned whether Lord Hutton's "bald conclusions" on the dossier's production could be reconciled with the balance of the inquiry's evidence.
BBC has questioned Lord Hutton's
And he asked whether enough weight was given to Dr Kelly's taped conversation with Newsnight's Susan Watts.
Following the publication of Lord Hutton's findings, Dyke said the corporation apologised for key things Gilligan got wrong in his broadcasts.
But he added that Dr Kelly was a credible witness whose views the public had a right to know.
Ex-BBC chairman Sir Christopher Bland warned earlier on Thursday against mass resignations and called for a period of reflection at the corporation, the broadcaster reported.