His dramatic resignation followed those of Davis and his deputy Steve Banker overnight over May's plans to keep Britain economically close to the bloc.
May has faced a backlash over the plan from Brexit hardliners in her Conservative Party who say it gives too many concessions to the European Union, but she has support from moderates and there has been no challenge to her leadership.
"Good riddance, Boris Johnson" reads the headline on an online opinion piece by the New York Times' editorial board.
Both MPs pointed to the Northern Ireland backstop, which the government signed up to in December, as a key part of how the government had ended up with what they argued was an unacceptable compromise.
Johnson had been due to host a summit about the western Balkans on Monday afternoon but was instead holed up in his official residence with close advisers, considering his position. "The trouble is that I have practised the words over the weekend and find they stick in the throat", he wrote to May.
Hunt said it was a moment to show that Britain remained a "strong, confident voice in the world".More news: A new - and affordable - Microsoft Surface tablet might arrive this week
Brexit negotiations with Brussels are also expected to resume next week.
Boris Johnson quit his post yesterday, following the earlier resignation of Brexit Secretary David Davis, putting the government in a tight spot with less than nine months left to complete the complex Brexit negotiations.
Margaret Thatcher initially supported the 1975 referendum on the U.K.'s European Union membership, but a string of firings and resignations of cabinet members (sound familiar?) who favored more integration against her wishes led to her downfall.
The ERG's chair, Jacob Rees-Mogg, has repeatedly made clear in recent days that he does not believe a change of leader is the right approach, but he has also suggested he and his colleagues could not back the Chequers deal in parliament.
Davis himself said it would be "wrong" for his departure to trigger a major party rebellion against May.
To trigger a no-confidence vote in the PM, 15% of Tory MPs must write to the chairman of the backbench 1922 Committee, now Sir Graham Brady.More news: White House announces additional $200B in tariffs targeting China
The pound pared losses amid fading concerns that the resignations will immediately push May to a confidence vote. However, should she survive such a challenge, Conservative Party rules prevent her opponents from making another try to unseat her for at least a year.
Her proposal would see Britain adopt European Union rules for trade in goods after Brexit, but maintain flexibility for its key services sector and end freedom of movement. The same paper also indicates that the United Kingdom will leave the EU's joint agricultural and fisheries policy.
Following Monday's resignations, EU President Donald Tusk tweeted: "Politicians come and go but the problems they have created for people remain".
Davis is the sixth Cabinet minister to resign from May's government in eight months, following former worldwide development secretary Priti Patel, defence secretary Michael Fallon, her deputy Damian Green, education secretary Justine Greening, and home secretary Amber Rudd.
However, those appeals were rejected by one of the leading pro-EU figures on the Labour benches, Wes Streeting, who said the Chequers deal was "dead".
The Johnson resignation was unnecessary - even Davis commented that Brexit was not essential to Johnson's portfolio - but he was likely more interested in jumping on the Brexit resignation bandwagon to see if there was a political opportunity to seize the premiership he has coveted for so long.More news: Barcelona Confirm Paulinho Loan Deal To Guangzhou Evergrande
"We do have a lot of allies, but we can't be taken advantage of", he said.