Mr Hunt was forced from his role as foreign secretary and his supporters were rounded on by the freshly-anointed Tory leader.
Meanwhile, Sajid Javid has been made Chancellor of the Exchequer.
Dominic Raab has been appointed Foreign Secretary.
Priti Patel becomes Home Secretary and Stephen Barclay remains in his role as Brexit Secretary.
Mr Johnson sacked Liam Fox as international trade secretary and Penny Mordaunt as defence secretary.
Both had backed Mr Hunt, while Dr Fox had gone a step further in criticising Mr Johnson's Brexit plan.
Scottish Secretary David Mundell, who previously said he would find it "extremely difficult" to serve Mr Johnson, tweeted that he was "disappointed but not surprised" to be departing.
Also leaving the frontbenches after Mr Johnson was formally appointed as PM by the Queen were Hunt-backer Damian Hinds, who was education secretary, and Business Secretary Greg Clark.
Mr Clark had recently warned that "many thousands" of jobs would be lost in a no-deal Brexit, which Mr Johnson has declined to rule out.
Northern Ireland secretary Karen Bradley is also understood to have been sacked after Mr Johnson entered No 10.
Foreshadowing his arrival, prominent no-deal critics chancellor Philip Hammond, international development secretary Rory Stewart and justice secretary David Gauke all quit.
So did David Lidington, who was effectively Theresa May's deputy prime minister.
Mr Hunt said he would have been "honoured" to continue at the Foreign Office but decided to return to the backbenches despite Mr Johnson having "kindly offered" him a different role.
He was forced out despite saying he would happily welcome his opponent to his Cabinet during the leadership race.
Ms Mordaunt's sacking so shortly after the Brexiteer became the first woman to head the Ministry of Defence came as a shock for many.
Secretary of state for housing, communities and local government James Brokenshire was also out, as was the much-criticised transport secretary Chris Grayling.
It is understood that Mr Grayling resigned.
Leader of the house Mel Stride was also returning to the backbenches, as was immigration minister Caroline Nokes.