The reshuffle also saw Environment Secretary Therese Coffey step down, saying in her letter it is time to "step back", with former Health Secretary Steve Barclay replacing her.
Victoria Atkins has stepped into Barclay's old role in the Department of Health, while Richard Holden has replaced Greg Hands as party chairman.
Speaking ahead of the reshuffle, a No10 source told GB News that Rishi Sunak "wants a united team to deliver the changes this country needs for the long term."
WATCH: Christopher Hope discusses Suella Braverman
In a brief statement after his appointment, Cleverly said: "It is an honour to be appointed as Home Secretary. The goal is clear. My job is to keep people in this country safe."
Asked if he wants to distance himself from the language used by his predecessor Suella Braverman, Cleverly told broadcasters: "I intend to do this job in the way I feel best protects the British people and our interests."
But hitting out at Sunak's decision to put Cleverly in the Home Office, a source on the right of the party said he "does not have the calibre to deal with the Home Office", warning: "It is the most challenging department by far".
They added: "People are right when they say he is a great guy, but that does not make a great Home Secretary."
Former Conservative MP Neil Parish said the Prime Minister should “prepare for war” following the sacking of Suella Braverman.
He told GB News: “Rishi Sunak better prepare for war I think because of course she is very much, Suella, the standard bearer of the right of the party.
“Now, I can understand, as Home Secretary she was probably ill-advised to make these comments, the problem is she does reflect a lot of opinion in the country and it will be very interesting now to see what happens, but I suspect Rishi Sunak in the end was left with no alternative.
“But I would have thought she would have been reshuffled rather than sacked but it's an interesting situation politically for Rishi Sunak, the Government, and the Conservative Party.”
MP Philip Davies added: "It is very disappointing that Suella is no longer Home Secretary - I like her and agree with her on virtually everything.
"However, I think we should also accept that she got herself sacked. You can’t go off-piste and just do your own thing without clearance without consequence.
"No Minister is more important than collective responsibility and we should be annoyed that Suella put the PM in an impossible no-win situation.
"I always said I would remain on the backbenches so I could do and say what I want - you can’t be in Government and do that. You have to pick a lane. What is important is the policies the Government pursues and there is no reason to think that on immigration and protests there will be a change in policy from that presided over by Suella.”
In a statement following his appointment, David Cameron said: “I may have disagreed with some individual decisions” made by Rishi Sunak, but added that he “is a strong and capable Prime Minister, who is showing exemplary leadership at a difficult time”.
He said: "The Prime Minister has asked me to serve as his Foreign Secretary and I have gladly accepted.
"We are facing a daunting set of international challenges, including the war in Ukraine and the crisis in the Middle East.
"At this time of profound global change, it has rarely been more important for this country to stand by our allies, strengthen our partnerships and make sure our voice is heard.
"While I have been out of front-line politics for the last seven years, I hope that my experience – as Conservative Leader for eleven years and Prime Minister for six – will assist me in helping the Prime Minister to meet these vital challenges."
Schools minister Nick Gibb was the second to go in today's reshuffle, after Braverman, announcing on X that he had asked the Prime Minister to step down from his role so he can prepare to take a diplomatic role after the general election.
He said he remains "an enthusiastic supporter of the Prime Minister's leadership".
Parliamentary Under-Secretary of State for Primary Care and Public Health Neil O'Brien also announced his departure this morning, saying: "With so much going on locally I want to focus 100 per cent on constituency work", saying he asked to go to the backbenches.
Health minister Will Quince and Paymaster General and Minister for the Cabinet Office Jeremy Quin also stepped down.
While many moderates in the party were demanding Braverman be sacked over her unauthorised Op-Ed, she is said to have the backing of as many as 52 Conservative MPs, many of whom come from the New Conservatives Group of MPs and the Common Sense group.
A source on the right wing of the party told GB News that the Conservative Party is "in disarray", warning that Sunak is facing threats from MPs who are of the view that it is "every man for himself" ahead of the next election.
Reacting to this morning's resignation, Conservative MP Andrea Jenkyns tweeted: "I support @SuellaBraverman Sacked for speaking the truth."
She added: "Bad call by Rishi caving in to the left".
A former minister told GB News that Sunak's decision to sack her is "surprising" noting that the former Home Secretary has "a lot of support" in the party.
But reacting, Kwasi Kwarteng told GB News: "Big news. High risk. But I think number of her supporters is exaggerated”.
Throwing his weight behind the move, Tobias Ellwood said the PM "now has an opportunity to regroup his Cabinet with a clear centre-right vision that looks beyond our party base.”
But there are understood to be between 30 and 50 MPs, many of whom are linked to the New Conservatives Group of MPs, who will push back against Sunak in the wake of his decision to sack her.
Speaking last week, tory MP Miriam Cates, a prominent member of the New Conservatives, said she "fully supports" the Home Secretary's Op-Ed.
Speaking to the Sun, Sir John Hayes called her the party’s “only hope”, while Jacob Rees-Mogg told his GB News show that "the calls to sack her seem to be disproportionate".
Meanwhile, former Conservative party leader Iain Duncan Smith told GB News she was right to take a stand against the pro-Palestine protests scheduled to take place over the weekend.
He said it would be "entirely reasonable" to - rather than ban the protests - simply ask them to postpone until Monday, saying the police could easily justify the decision through the fact that Remembrance Sunday is already a major event and takes a large amount of policing capacity to monitor.
There is also support for Braverman outside of the New Conservatives, with one former minister on the right wing of the party saying Braverman was "voicing the concerns of many colleagues" with her Op-Ed.
David Cameron's appointment has triggered backlash from the right of the Conservative party, with a source warning that the appointment is "utterly bonkers".
Reacting to the news, the insider said: "It just shows the lack of strategy - why have we campaigned for change as our main theme and then brought back Cameron?"
They added: "Also, what about all his dodgy dealings after leaving PM and just watch out for his ties with China.