The Conservatives said Mr Sunak is carrying out a wider reshuffle which “strengthens his team in Government to deliver long-term decisions for a brighter future”.
But sacking one of the leading figures on the Tory right could pose difficulties for the Prime Minister as he seeks to get his party united behind him and ready for a general election expected next year.
Mrs Braverman said: “It has been the greatest privilege of my life to serve as home secretary.”
Ominously for Mr Sunak, she added: “I will have more to say in due course.”
Mr Cleverly’s appointment as Home Secretary leaves a vacancy in his former role of foreign secretary.
And in a move which raised eyebrows across Westminster, former prime minister David Cameron was seen in Downing Street, raising speculation that he could be in line for a dramatic return to government – potentially at the Foreign Office.
News of Mrs Braverman’s exit came as defence minister James Heappey was touring broadcast studios.
Minutes before she was sacked, he had told LBC that Mr Sunak and his team in No 10 had been “very clear she (Mrs Braverman) has his confidence and, in that sense, one would imagine that she will continue”.
But he was told on air during an ITV Good Morning Britain interview that she had been sacked, leaving him to say: “Your viewers will be enjoying my discomfort, but it is in this case difficult to offer commentary when I just don’t know what is going on.”
Liberal Democrat leader Sir Ed Davey said: “Suella Braverman was never fit to be Home Secretary. Rishi Sunak knew this and he still appointed her.
“It was the Prime Minister’s sheer cowardice that kept her in the job even for this long. We are witnessing a broken party and a broken Government, both of which are breaking this country.”