In a letter to Hammond, Carney says: "I recognise that during this critical period, it is important that everyone does everything they can to support a smooth and successful Brexit".
Hammond said the government was devoting all its efforts to securing a deal on a new relationship with the European Union before Britain leaves the bloc in March next year but admitted the clock was ticking. He extended it by a further year in the aftermath of the Brexit vote.
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".
Before Carney joined the BoE in July 2013, he said he only wished to serve five years of the standard eight-year term for a BoE governor to minimise his children's time away from their native Canada.
The governor and Prime Minister have clashed in the past with May commenting in 2016 on how there would be "bad side effects" for Carney's monetary policy and Carney taking a negative view on the future of Brexit.
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.
The extension isn't the first of Carney's tenure at Threadneedle Street.
"A governor who was leaving at the end of June, with his bags already packed, would be in a poor position to represent the United Kingdom in what might be some quite critical - and time critical - negotiations over that period".
Sir Jon Cunliffe, the deputy governor with responsibility for financial stability, has also been re-appointed, it added.