Sir Mervyn King will retire next June and George Osborne said that Sir Mervyn's successor would have to undergo a "fair and open" application process before being annouced at the end of the year.
The advert will run in the Economist magazine on Friday and then be published on the Public Appointments website.The closing date for applications is 8 October.
In the advert the Treasury will say: "The new governor will lead the Bank through major reforms to the regulatory system, including the transfer of new responsibilities that will see the Bank take the lead in safeguarding the stability of the UK financial system."
To qualify for the job, a candidate must "have experience of working in, or with, a central bank or similar institution; or will have worked at the most senior level in a major bank or other financial institution".
Following the advertisement of the role, an interview panel chaired by Sir Nicholas Macpherson, the permanent secretary to the Treasury, will interview the shortlisted candidates.
The new governor will start on 1 July, 2013, and - as per changes likely to be made law in the Financial Services Bill - will be appointed for a single eight-year term.
Responding to the Chancellor’s comments regarding the appointment process for the next Governor of the Bank of England, the Chairman of the Treasury Select Committee, Andrew Tyrie MP, said: "Today’s announcement in the House of Commons was welcome. Further detail is required.
"The choice of the next Governor is the most important public appointment the Government will make.
"That is why the Treasury Select Committee will both scrutinise the selection process closely and subject the Government’s preferred candidate to what would amount to a full pre-appointment hearing.
"The legitimacy of any candidate who passes that test can only be enhanced."
