After being moved sideways in Carney's management reshuffle earlier this year, the protege of ex-governor Mervyn King said he was severing ties with Threadneedle Street after 25 years.
Dale became the Bank's executive director for financial stability, strategy and risk after a job swap with Andy Haldane, losing his place on the monetary policy committee (MPC), the nine-strong body that sets interest rates.
Sources close to Dale said his departure was not linked to any failure to get on with Carney or a sense that he had been snubbed. "The job offer to become chief economist at BP came up in recent days and, at 47, Spencer felt that opportunities of that sort did not come along that often."
As chief economist, Dale was responsible for the Bank's forecasts that inform the MPC's decisions. He moved to his new job at the Bank at the start of June, but will leave at the end of October.
Carney said he had been privileged to work closely with Dale. "He is an immensely talented and committed public servant, who has made significant contributions to monetary and financial stability over the course of his career at the Bank."
He added: "As the Bank's chief economist, Spencer has played a key role in ensuring that the monetary policy committee operates as an effective policy-making body, and more recently, has brought that same rigour and dedication to the financial policy committee."
Dale said: "It has been a huge privilege to serve the Bank of England over the past 25 years. It has also been an honour and a pleasure to work with so many talented people committed to serving the public good. This is a tremendous institution that has changed remarkably since I joined, and whose additional responsibilities mean it has a central role in ensuring economic and financial stability for the UK.
"To truly make the most of these new powers, I fully support the Bank's objective to act as a single, cohesive policy institution. I will miss the Bank greatly and I wish I could have stayed longer to contribute more. But the opportunity to work in a different environment with one of the UK's pre-eminent companies was simply too good an opportunity to refuse."
guardian.co.uk © Guardian News and Media Limited 2010