Theresa May is still the prime minister and is due to chair a meeting of her new-look cabinet.
Hunt, 51, a member of the British Conservative Party, has been the longest-serving health secretary in British history-holding the position from 2012 to date-and he was elected member of parliament in 2005 to represent South West Surrey.
In a resignation letter to the Prime Minister, Boris Johnson said that Britain appeared to be "heading for a semi-Brexit" and would take on "the status of a colony" under her plans.
He said in his letter that May's plan to keep close economic ties with the bloc mean the United Kingdom was heading for a "semi-Brexit" that would leave Britain with the "status of colony" within the EU.
Theresa May has issued a reply to Boris Johnson's resignation letter in which he was critical of the Prime Minister's Brexit strategy.
The Brexit "dream is dying, suffocated by needless self-doubt", he said in the letter, which he posted to Twitter.
With Britain due to leave the 28-nation bloc on March 29, 2019, European Union officials have warned Britain repeatedly that time is running out to seal a deal spelling out the terms of the divorce and a post-split relationship.
Addressing parliament just minutes after her office announced that Johnson, the face of Brexit for many in Britain, had quit, May told MPs she appreciated the work of her two ministers.
However, she said that if he was unable to support the Government's agreed position "it is right that you step down".
In recent weeks, junior ministers Phillip Lee and Greg Hands have also resigned in order to vote against government - the former over Brexit, the latter over Heathrow.
Staunch Brexiteer Dominic Raab was named as Mr Davis's replacement as Secretary of State for Leaving the EU.
Government unity began to fray within hours.
He said: 'We are now in the ludicrous position of asserting we must accept huge amounts of precisely such European Union law, without changing an iota, because it is essential for our economic health - and when we no longer have any ability to influence these laws as they are made.
Less than nine months remain until Britain reduces the EU's membership on March 29, 2019.
May's supporters worry that more ministers could resign, and pro-Brexit lawmakers from her Conservative Party could trigger a no-confidence vote in the prime minister.
David Davis quit as Brexit Secretary on Sunday.
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