An Executive Fellow of Economics at the School, Broadbent is due to take over from Charlie Bean when he retires at the end of June following 14 years of service at the Bank.
Broadbent has been a part of the Bank's Monetary Policy Committee since 2011 when he joined as an external member.
He has previously worked as an economist at Goldman Sachs, an economic adviser to the Treasury, and an assistant professor of economics at Columbia University from 1997-2000.
Other new appointments at the Bank's top table include Nemat Shafik, who takes on the newly-created role of deputy governor for markets and banking.
Anthony Habgood, the chairman of Whitbread, which owns Costa Coffee and Premier Inn, also becomes chairman of the court of the Bank of England.
The Bank's Governor Mark Carney said: "I am delighted that individuals of the calibre of Ben Broadbent, Minouche Shafik and Anthony Habgood will be joining the Bank's leadership group.
"With a diverse combination of skills and experience, these appointments result in a well-rounded senior management team at the Bank - one that will set the direction for an ambitious agenda of transformation for the institution and enable it to meet the challenges and opportunities it faces in maintaining monetary and financial stability."