The Hutton report will impact on the renewal of the BBC's charter, said Culture Secretary Tessa Jowell.
Appointment of BBC chairman would be 'completely impartial'
The inquiry and charter renewal were separate processes but where it was "relevant and appropriate" the Hutton conclusions would be incorporated.
One of the first jobs of the new BBC chairman would be to "take those conclusions and subject them to discussion" within the corporation.
Gavyn Davies' successor would be chosen completely impartially, she said.
"I said last summer when the Hutton inquiry was established that charter review and the Hutton inquiry were two separate processes and they are, except that of course it's relevant and appropriate that Lord Hutton's conclusions - his specific conclusions in relation to the BBC - are incorporated in that process," she told the BBC.
"One of the first jobs of the new chairman will be to take those conclusions and to subject them to discussion, scrutiny within the governors and within the BBC, and then report back as part of the process of developing the conclusions at charter review."
Mr Davies quit his job as BBC chairman after the Hutton report criticised the corporation for its role in the David Kelly affair.
The weapons expert apparently committed suicide after being named as the source for a BBC story about the government's case for war with Iraq.
Director General Greg Dyke also quit the corporation on Thursday.
Ms Jowell said that Mr Davies had been the first chairman of the BBC to be appointed independently.
She said that the process to appoint his successor would "not be subject to any interference".
The post would be advertised, applications invited and then an interview board, chaired by the top civil servant at the Department for Culture, would make a recommendation, she said.
That would then be passed to the prime minister for approval and then finally to the Queen.
Ms Jowell pledged the government would be quick to get a new chairman appointed.
Asked if the government had been damaged by the Kelly affair as well as the BBC, she said: "I think that must be the case and I think that the polls reflect that.
"That's why it's important that both the government and the BBC move on - and move on in a way that reconnects with a public that we exist to serve and rebuilds trust through that process."