This is the original radio announcement on the Italian radio from July 25, 1943 at 10:45pm:
[My translation:] “Attention! Attention! His Majesty the King and Emperor, [Victor Emmanuel III,] has accepted the resignation of the Head of Government, Prime Minister, and Secretary of State, Mr. Benito Mussolini, and has appointed to [these same offices] His Excellency, Marshal of Italy Pietro Badoglio.”
The bloodless coup that had occurred the day before was in no small measure the brainchild of a now forgotten Italian politician: Dino Grandi, 1st Count Mordena.
Dino Grandi had been one of “Il Duce”s earliest companions. Originally he had left-wing sympathies like Mussolini himself (many people forget that “Il Duce”s first major political engagement was as the editor-in-chief of the Italian socialist newspaper Avanti! [Forward!]). Like in “Il Duce”, World War One awakened nationalist tendencies in Grandi. He was one of the 35 Fascist delegates elected to the Chamber of Deputies in 1921. From September 1929 until July 1932, he served as Foreign Minister, in which position he apparently possessed some skill: particularly with the United Kingdom, the anglophile Grandi built up good relations.
Considering Grandi’s attitude to the League of Nations too accommodating, Mussolini dismissed him and took up the portfolio himself, before later passing it on to his son-in-law Galeazzo Ciano (whose diaries are a valuable primary source).
Grandi was appointed ambassador in London as a kind of consolation prize. He reportedly had affairs with a number of high-society ladies, notably Lady Alexandra Curzon, the daughter of Viceroy of India, Lord Curzon. (Said daughter simultaneously was carrying on with both British Union of Fascists leader Oswald Mosley and with the Foreign Secretary, Viscount Halifax).
At the outbreak of the war, Grandi was recalled when Hitler found out about Grandi’s attempts to negotiate a separate nonaggression pact between Italy and the UK, and went ballistic on Mussolini. The latter appointed Grandi Minister of Justice upon his return. Later he became Chair of the lower house of the quasi-parliament, the Chamber of Fasci and Corporations [“corporations” in the sense of estates, professional associations, and the like — in keeping with Mussolini’s “corporatist” ideology].
Grandi opposed both antisemitic legislation (introduced in 1938 under Nazi pressure) and Italy’s entry into the war, and his increasing criticism of Mussolini’s policy led to his ouster from the cabinet on February 5, 1943. Crucially for what follows, however, he remained a member of the Grand Council of Fascism.
By this time, the continued military bad news from the Eastern Front and North Africa had reduced Mussolini to a state of near-catatonia, and increasingly, senior Fascists started grumbling that Il Duce had become unfit for the job.
Now much unlike the Führer — who was accountable to no-one (except arguably Satan) — Mussolini still had a measure of accountability to the Grand Council of Fascism, as well as to the head of state, King Vittorio Emanuele III. The latter, under Article 5 of the Statute Albertino (the constitution of Sardinia and later of Italy until 1948), had the constitutional prerogative to appoint and dismiss all government officials, including the Prime Minister: he was, however, reluctant on principle to exercise this power.
Then, on July 10, 1943, the Allies invaded Sicily, which was the last straw for Grandi, Ciano, and many others. Grandi, as the bearer of the country’s highest decoration, had free access to the king and sounded him out. An agreement was reached that, if the Grand Council of Fascism were to recommend Mussolini’s dismissal, then the king would carry it out.
Grandi scheduled a meeting of the Grand Council of Fascism on Saturday evening, July 24, 1943 at its usual location in the aptly named “Sala del Pappagallo” (Parrot Room, after the parrot Pope Paul II had kept there https://www.romasegreta.it/campitelli/piazza-venezia.html [in Italian]) of the Palazzo Venezia on San Marco Square. The ostensible reason was the presentation to Mussolini of a new book.
There, within sight of the Forum as well as of Trajan’s Market, the Duce was suddenly presented with a motion to invoke Article 5 (implied: for the King to dismiss Mussolini).
Following a lengthy debate and a break, the 28 members voted by roll call on Grandi’s motion: 19 voted in favor, 7 against, 1 abstained, and one left the room. At 2:40am on July 25, the council broke up for what turned out to be the last time.
Mussolini requested an audience with the king, who agreed to receive him at 5pm. There and then, he was told he was dismissed from his offices and that Marshal of Italy Pietro Badoglio had been appointed in his place.
Upon emerging from the palace, a specially briefed detachment of Carabinieri accompanied the Duce “for his own protection” to a military ambulance that turned out to be a disguised “Black Maria” taking him to prison.
And thus ended the reign of Il Duce. Two months later, an SS commando team led by Otto Skorzeny would spring him from imprisonment. Brought to Hitler, he was told he would now be the head of a puppet state in the German-occupied zone of Italy (what became known as the “Italian Social Republic”). Mussolini was at that point ill, exhausted, and looking forward to retirement, but the German tyrant threatened to have several Northern cities flattened by the Luftwaffe unless he consented. So he spent the remaining fewer than two years of his life a nominal dictator, but a prisoner in fact.
As for Dino Grandi, he fled abroad to Portugal and then Brazil — where he became a successful businessman — but eventually would return to Italy and die there at a ripe old age.