In a tweet, Sunak said that the public rightly expect government to be conducted "properly, competently, and seriously." He also added that this may be his last ministerial job, and that he "believed these standards are worth fighting for."
The ministerial exits will come as a big blow to Johnson's leadership and follow a day of high political drama since a former civil servant spoke out about Downing Street's handling of allegations against recently suspended MP Chris Pincher.
The resignation came soon after Johnson said he "bitterly regrets" giving Chris Pincher a government role as deputy chief whip after being made aware of a misconduct complaint against him.
'You Have Lost My Confidence': Sajid Javid
In the resignation letter to Johnson, Health Secretary Javid said that it was clear to him that "this situation will not change under your leadership -- and you have therefore lost my confidence too".
Javid, who is a British citizen of Pakistani origin, also stated, "We [Conservative party] may not have always been popular, but we have been competent in acting in the national interest. Sadly, in the current circumstances, the public are concluding that we are now neither.
"The vote of confidence last month showed that a large number of our colleagues agree," he wrote in his letter.
In June this year, Johnson successfully survived a trust by winning the backing of 211 out of 359 Conservative lawmakers.
In 2019, a year before the pandemic Johnson steered the party to its biggest general election mandate in more than three decades.