According to the Financial Times, May gave her approval to the idea which would likely see Carney remain in the role until the second half of 2020.
Carney was originally scheduled to step down in June 2019, but U.K. Treasury chief Philip Hammond, the chancellor of the Exchequer, said in a letter to Carney that the.
He also drew the ire of pro-Brexit lawmakers who believe he waded too far into the political debate, and has been accused of botching messages on policy for most of his time at the bank. Following Britain's Brexit vote, he agreed to remain in place an additional year to the end of June.
Her spokesman said May saw an informal European Union summit in Salzburg next week as a "staging post" in Brexit negotiations that would allow European Union leaders to discuss her proposals for the first time. His new exit date effectively wipes out speculation he planned to run in the nation's next federal election, which has to be held by October 2019 at the latest.
The re-appointment is officially made by the Queen, on the advice of Hammond and the prime minister, Theresa May. The extension was also welcomed by Nicky Morgan, the chair of the parliament committee which monitors the BoE and the finance ministry.
In remarks that will remind Brexiteers why they find him so frustrating, Mr Carney warned that a no deal Brexit would send prices rising and hit real incomes.
In a letter to the Chancellor, Carney said: "I recognise that during this critical period, it is important that everyone does everything they can to support a smooth and successful Brexit".
"I am willing to do whatever I can in order to promote both a smooth Brexit and an effective transition at the BoE".
Should Brexit go smoothly and United Kingdom economic activity pick up steam in 2019 a Carney-led Bank of England would nearly certainly accelerate the pace of interest rate rises as per recent guidance.
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.