BBC News Online explains how the process works.
Gavyn Davies was appointed chairman in 2001
The BBC's chairman, like the rest of the corporation's 12-strong board of governors, is officially appointed by the Queen. But in practice, this appointment is made by the government.
Michael Grade and his predecessor Gavyn Davies were chosen by Culture Secretary Tessa Jowell, with the prime minister giving his the final approval before their choice was submitted to the Queen.
But the process is designed to make sure the contest for the job is as fair as possible - and to guard against the government merely picking its own candidate.
As an extra measure Culture Secretary Tessa Jowell has announced that the Commissioner for Public Appointments, Dame Rennie Fritchie, and three senior privy councillors will oversee the appointment to ensure there is public confidence that the process is independent.
The appointment takes place under the Nolan rules - established by the government's Committee on Standards In Public Life.
It was set up 10 years ago, in the wake of the "cash for questions" scandal which damaged John Major's Conservative government.
The rules are named after Lord Nolan, the committee's first chairman.
The job is advertised, as the rules recommend as many methods as possible should be used to find suitable candidates.
An independent panel looks at the applications, and then draws up a shortlist of candidates.
The panel will make its recommendations to Tessa Jowell
The panel is headed by a senior civil servant - the committee which recommended Gavyn Davies was led by Nicholas Kroll, who was then the acting permanent secretary at the Department for Culture, Media and Sport.
Mr Davies' panel included Reuters chairman Sir Christopher Hogg, zoologist Sir Brian Follett and Liz Forgan, a former managing director of BBC network radio, as well as an independent assessor.
Candidates will then be interviewed by the panel, which will then make its final recommendations to Tessa Jowell.
Dame Rennie Fritchie, whose office oversees some 11,000 quango and public company appointments, will monitor the process through a scrutiny panel.
Richard Ayre, a former controller of BBC editorial policy, is among critics who think politicians are still too close to the appointment.
"There is only one way to reassure the public - the appointment has to be taken out of the hands of Tessa Jowell and it has to be put firmly into the domain of the commission for public appointments," he told BBC News 24.
"Take it out of the hands of politicians altogether - or a sceptical British public will think it is made for political reasons."
But Ms Jowell is adamant the current procedures are the right ones.
"Gavyn Davies was the first chairman of the BBC to be appointed under a fully independent process - the interviews are carried out by people of standing and who are independent of ministers," she told BBC One's Breakfast.
"All this is carried out under very well established rules, in order to promote the independence and transparency of such appointments.
"This will not be an appointment subject to interference."