Hammond also confirmed that Carney, who said last week he was prepared to stay in his job beyond next June when his term was due to end, had agreed to remain until 2020.
Carney was previously set to leave his role in June 2019 but has been persuaded to stay on by Chancellor Philip Hammond.
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"I fully recognise that during this critical period, it's important that everyone does everything they can to help with the transition of exiting the EU", Carney said.
The United Kingdom will leave the European Union on March 29 but as yet no full exit deal has been agreed and many lawmakers in Prime Minister Theresa May's own party object to her own so-called Chequers proposals.
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"I deeply appreciate your support and that of the Prime Minister".
Mark Carney is sticking around for Brexit.
"Accordingly, I am willing to do whatever I can in order to promote both a successful Brexit and an effective transition at the Bank of England". However, it is understood they now have a good relationship.
"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". He extended it by a further year in the aftermath of the Brexit vote.
"In a sea of Brexit political pygmies the governor of the Bank of England is one of the only sane voices at the table, so it is welcome news he is staying on".
Carney took over from Mervyn King as Bank of England governor in 2013, initially committing to a five-year term despite traditional protocol dictating an eight-year term as governor.