Mr Sunak, Chancellor since February 2020, has long been considered a natural heir to succeed Mr Johnson as the future leader of the Conservative Party.
He tendered his resignation on Tuesday evening, saying: “I am sad to leave the government, but I have reluctantly come to the conclusion that we cannot go on like this.”
He went on to say that the public “rightly expects government to be properly, competently and seriously” and added that “these standards are worth fighting for”.
Earlier this year, Mr Sunak’s leadership credentials were tarnished by a backlash over his wife’s non-resident tax status and the revelation that he had a US green card while still Chancellor.
However, his low-tax, Thatcherite instincts are popular with Conservative members and his popularity with members has risen again this month amid a wealth of measures to support Britain through the cost of living crisis.