In his resignation letter, Sunak said the government should be run properly and seriously.
Health Secretary Sajid Javid resigned in protest.
After the announcements, the British pound fell to a new low. The currency hit 1.1923 against the dollar during the day.
Sunak said that the public expects government to be conducted well.
I think these standards are worth fighting for and that's why I'm quitting.
In a letter to the prime minister, Sunak said that he was sad to be leaving government but that he had come to the conclusion that we couldn't continue.
Over the last few months, Johnson's leadership has been plagued by a series of scandals.
A vote of confidence was triggered by the prime minister's own lawmakers. He has continued to be dissatisfied with his leadership within his own party and beyond.
Despite public anger over a long and growing list of accusations, Johnson has refused to resign.
Chris Pincher is a Conservative lawmaker in the House of Commons. The former deputy chief whip was accused of drunkenly groped two men.
Minutes before the resignations, Johnson apologized for appointing Pincher as deputy chief whip despite knowing of an investigation into his behavior.
In May, a damning report into several high-profile Covid-19 lockdown-breaking parties, dubbed "partygate," was released, adding to calls for Johnson's resignation.
Javid wrote a letter to Johnson saying the recent vote of confidence was a chance for humility, grip and a new direction.
He said that it was clear to him that the situation would not change under his leadership.
CNBC contributed to this report.