Dyke stood down as Prime Minister Tony Blair called on the public broadcaster to make a full apology for the allegations it made during the weapons of mass destruction row.
Announcing the news, Dyke said he hoped their departures meant "a line can be drawn under this whole episode". The governors have appointed Mark Byford as acting director-general.
In his resignation statement, Dyke, said: "I am today announcing that I have resigned from the BBC. My position as director-general has inevitably been compromised by the criticisms of BBC management in the Hutton report. Following Gavyn Davies' decision to go, I felt I too should offer my resignation to the Board of Governors."
He added: "Throughout this affair my sole aim as director-general of the BBC has been to defend our editorial independence and to act in the public interest."
In a statement, the acting chairman Lord Ryder, on behalf of the board of governors, said: "Greg Dyke, the BBC director-general, has tendered his resignation to the board of governors and this has been accepted. Mark will retain responsibility for all pre- and post-broadcast programme compliance as announced with his appointment as deputy director-general in December 2003."
Dyke's decision to stand down follows a crisis meeting of the BBC governors this morning at which they discussed their response to the Hutton Report, which was damning of BBC editorial practices.
The report heavily criticised the BBC for "defective" editorial controls in relation to its defence correspondent Andrew Gilligan's broadcasts on the 'Today' programme.
Earlier today Blair demanded a full apology from the BBC and said he expected further action to be taken by the broadcaster. His wish has been answered.
However, many already see the outcome of the report as too one-sided and heaping an unfair amount of blame on the BBC, which is now paying the cost.
It is expected that both BBC news and current affairs chief Richard Sambrook and reporter Gilligan will also lose their jobs.
The secretary of state for culture, media and sport Tessa Jowell has announced that the process for appointing a new chairman will begin shortly and Byford has said that he will not be putting forward his name for the position on a permanent basis.
The board of governors said in a statement that Davies and Dyke would be greatly missed by the board of governors, the executive committee and the management and staff with whom they worked.
Lord Ryder, said: "The manner of their departures demonstrates the integrity of both men. The whole corporation owes them a debt of thanks and they deserve enormous credit for their dedication and contributions to the BBC over the last few years.
"Finally, on behalf of the board, I want to express my thanks to the staff of the BBC for their continued commitment to the principles of public service broadcasting and especially to those with the vital task of reporting the Hutton Inquiry outcome accurately and impartially."
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