Hammond also said that Carney would provide "vital stability" for Britain's economy during the Brexit transition.
The decision also raises questions about the government's grasp of the Brexit process if Carney's presence is needed to ensure stability, or the United Kingdom treasury is struggling to find a replacement while it focuses on negotiations.
In addition, the Treasury announced that Jon Cunliffe was reappointed for a second five-year term as deputy governor responsible for issues relating to financial stability.
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 says: "Accordingly, I am willing to do whatever I can in order to promote both a successful Brexit and an effective transition at the BoE".
"I deeply appreciate your support and that of the Prime Minister".
In his letter today, the chancellor explained that Mr Carney's extension was entirely Brexit related.
The announcement from the government and England's central bank was expected after Governor Carney told lawmakers last week that he was "willing" to extend his tenure beyond his previously scheduled June 2019 departure.
Having an inexperienced leader at Threadneedle Street at such a moment would nearly certainly be unhelpful.
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.