Hammond said Carney would provide "vital stability" for Britain's economy during the Brexit transition and the extension was also welcomed by Nicky Morgan, the chair of the parliament committee which monitors the BoE and the finance ministry.
Labour MP Virendra Sharma, a champion of the anti-Brexit campaign group Better for Britain, said Carney's willingness to stay through the turbulence "shows the problems that the government are having on Brexit".
Chancellor of the Exchequer Philip Hammond ended days of speculation on the governor's future, telling lawmakers on Tuesday that the Canadian won't step down as planned in June 2019.
A senior government figure said: "The PM thinks he has done a good job in hard circumstances; he is well respected and has a good worldwide standing".
Ottawa Senators trade Erik Karlsson to San Jose Sharks
Will they be allowed to grow at their own pace, rather than being judged prematurely, with unrealistic expectations attached? Once upon a time, Montreal Expos fans experienced the type of hollow feeling that hit Senators faithful Thursday.
"I deeply appreciate your support and that of the prime minister".
Carney had been due to stand down in June 2019, after a six-year tenure at the top of the central bank.
Nigel Farage wasn't happy with the announcement that the Governor of the Bank of England is staying on until 2020.
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.
Last November the BoE raised rates for the first time in more than a decade and increased them again last month, when Carney said that market expectations of a further rate rise a year for the next few years would be a reasonable rule of thumb.