Last month it was reported Carney had been asked by the Treasury to stay on another year in a move to settle the City's Brexit concerns.
The Bank of England has twice hiked interest rates under Carney's watch, most recently in August.
Bank of England Governor Mark Carney attends the central bank's financial stability report in central London on June 27, 2018.
In a letter he added: "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".
Carney confirmed last week that he was in talks with the Treasury over extending his tenure, saying he pledged to do "whatever he can to support the United Kingdom through Brexit".
Britain is due to leave the E.U.in March 2019 but there is uncertainty as to how exactly it will depart the trading bloc.
He had originally only meant to remain for five years after joining in 2013, but announced plans to stay an extra year four months after the Brexit Referendum in June 2016.
Nigel Farage wasn't happy with the announcement that the Governor of the Bank of England is staying on until 2020. He initially said he'd serve just five years of what is usually an eight-year term, but following the Brexit referendum agreed to remain in place an additional year to the end of June 2019.
"I am willing to do whatever I can in order to promote both a smooth Brexit and an effective transition at the BoE".