Writing in the BBC staff newspaper Ariel he told them that the apology was necessary following the departures of Gavyn Davies and Greg Dyke.
"It was necessary for Greg and me to apologise for the BBC's errors highlighted in the Hutton Report. Most of our mistakes were, of course, conceded during the inquiry itself," he said.
He added that Davies accepted ultimate responsibility by resigning and that Dyke also offered his resignation to the governors and it was accepted.
He said that the BBC must follow the lead established by Dyke in his email last week when he told staff that a line must be drawn under the whole affair.
"Now we must all set our eyes on the future in the public interest. We owe this duty to the BBC's audiences," he said.
Lord Ryder said that Mark Byford, the acting director general, would undertake a review of the lessons the BBC must learn from the last few months, including how the BBC investigated and corrected editorial mistakes.
He said that "impartiality, accuracy and trust" have always been core BBC values and promised that brave, independent and rigorous journalism would be maintained under Byford's leadership.
Lord Ryder also confirmed that its major document on Charter Review, due to be published in March, will be postponed until a new chairman and permanent director-general can take personal ownership of it.
He said that the Department of Culture, Media & Sport has assured the BBC that the vacant chairmanship will be filled by the middle of April, that the governors will invite applications for the director-general's job and that a shortlist will be drawn up after the new chairman assumes office.
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