Dr Posen, an American economist, has held the position since 1 September 2009 and has been particularly vocal in advocating increasing the Bank’s asset purchase programme.
The job, advertised on the HM Treasury website, is on a part time basis averaging three days a week. Appointments last a term of three years and are come with an annual salary of £131,771 plus healthcare benefits.
Candidates are required to have strong and proven economics knowledge and skills, analytical ability, independence of thought and interpersonal skills, communication skills and undisputed integrity and standing.
The current external committee members are Dr Posen, Dr Martin Weale, Prof. David Miles and Dr Ben Broadbent.
The Bank has also appointed three new non-executive directors to its Court to start in June.
Bradley Fried, Tim Frost and Dave Prentis will all assume the three-year term position on 1 June, replacing Brendan Barber, Harrison Young and Mark Tucker.
Mr Fried is a former chief executive of Investec, Mr Frost is founder of Cairn Capital and Mr Prentis is general secreteary of trade union UNISON.
Michael Cohrs, John Stewart and Adair Turner have all been re-appointed as non-executive directors but Lord Turner will cease to hold this position once the Financial Services Bill reform comes into place.
Sir David Lees, chairman of the Court of the Bank of England, said: "The non-executive directors play an essential role in overseeing the management of the Bank, a role that will become increasingly important as the Bank assumes its new responsibilities.
“I am delighted to welcome the appointment of the three new non-executive directors to the Court and the re-appointment of the three non-executives whose current terms are about to expire.”