Hammond also said that Carney would provide "vital stability" for Britain's economy during the Brexit transition.
Mr Hammond wrote to Mr Carney: "An extension of your term would ensure there is continuity at the Bank during this exceptional period and would also allow for a new Governor to be appointed during the Autumn next year after the terms of the UK's withdrawal and the framework for the future partnership have been finalised".
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He was seen as a key source of stability in the political power vacuum that followed the Brexit vote, with one former policy maker calling him the "only adult in the room" for his pledge to support the financial system in the immediate aftermath.
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Mr Carney had been due to step down from the role at the end of June 2019 - two years short of the eight-year term governors usually serve.
"I am willing to do whatever I can in order to promote both a smooth Brexit and an effective transition at the BoE".
Hammond added: "I'm delighted to announce the re-appointment of Sir Jon Cunliffe for a further term as Deputy Governor, and I'm confident his extensive experience will continue to be a valuable asset to the Bank of England". "Whoever would take over, had they taken over in June next year, or now its going to be January 2020, would be looking at a very gradual policy normalization, subject to the negotiations in terms of our relationship with the European Union".
FILE PHOTO: The Governor of the Bank of England, Mark Carney, speaks to the Scottish Economics Forum, via a live feed, in central London, Britain March 2, 2018.
"It is an important time and we have an important supportive role to make sure whatever Brexit the government negotiates, it is a success, and providing a measure of continuity should help that".