In a statement released on Friday morning, the Bank said Tucker would "provide support" to the new governor, before departing, initially to spend a period of time in US academia.
In his resignation letter to the chancellor, Tucker, one of the Bank's three deputy governors, said: "I am grateful to you for agreeing that I should step down slightly before the end of my term as a deputy governor of the Bank of England but after I have been able to provide support to the new governor in his first few months in office."
Tucker was appointed for a five-year term, which was due to come to an end next February. His name is now likely to be linked with top banking jobs, such as the soon to be vacant chairman's role at Lloyds Banking Group, which is 39% owned by the taxpayer and could be the first of the two state-backed banks to return to the private sector.
The outgoing governor, Sir Mervyn King, said: "Paul's contribution to the Bank, to monetary policy and more generally to public policy, both in the UK and in the world as a whole, has been enormous."
Many commentators had expected Tucker to leave the Bank after failing to secure the governorship – but it was a surprise that he announced his departure even before King's successor arrived, and will fuel speculation that Carney plans a radical shake-up of the Bank's personnel.
Carney, who has worked closely with Tucker at the international Financial Stability Board, which is re-writing global bank regulation, said: "I wish Paul every success in the next phase of his career and look forward to maintaining our close dialogue on how to build a more resilient financial system that more effectively serves the needs of the real economy."
George Osborne, whose decision to headhunt Carney from Canada thwarted Tucker's long-held ambition to lead the Bank of England, said: "I have no doubt that you will continue to make a towering contribution to the international economic community."
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