Nicknamed 'il martello' ('the hammer') in Italy, the stories of his intensity come thick and fast.
The flying water bottles, the repeated instruction that his players must 'eat grass', the words from Andrea Pirlo that 'when Conte speaks, his words assault you' – one wonders if Chelsea really have moved on from Mourinho, or whether it is a case of 'meet the new boss, same as the old boss'.
In the months since Mourinho left, and before Conte arrives, it has been very different at Chelsea.
It was Wesley Sneijder, who played under Guus Hiddink for Holland, that gave the 69-year-old the 'friendly uncle' tag.
Oscar recently agreed with that description, dubbing the stand-in Blues boss 'a very nice guy' and 'very smiley'.
Sneijder, by the way, described Hiddink's predecessor as the Dutch national coach – present Manchester United boss Louis Van Gaal, as a 'tough school teacher'. And Van Gaal is supposedly a soft touch compared with Conte.
So are Chelsea falling into the same old trap by going back to an intense disciplinarian after results picked-up under Hiddink?
Chelsea have tended to succeed under two sorts of bosses in recent years: with the permanent appointments often being 'bad cop', and the interims who replaced them more a case of 'good cop'.
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Those who got it most right have managed to combine the two.
Jose Mourinho, for example, is known for the ambiance of mutual respect he instilled with players – friendly text messages, taking an interest in their family situations, and the like.
But everyone who has played for him says he is the hardest taskmaster they have ever known.
The problem, as his second tenure showed in the way it came to an end, is when the latter of those assets totally eclipses the former.
Players will respond to calls for hard work, but seldom in these days of millionaire sportsmen, deliver if they think they are being bullied.
Carlo Ancelotti carried out a similar balancing act: appearing in public as the friendly, laissez-faire playboy – but again, on the training pitch, he drilled his team to perform.
Antonio Conte's playing honours
Claudio Ranieri, the former Blues boss on the brink of a miracle with Leicester, has the public image of a children's party entertainer. Yet here is another case of the behind-closed-doors reality being very different.
In the case of the interims, Chelsea have taken situations where the relationship between player and manager has all-but completely broken down, and sought to inject a bit of levity – a sort of emergency release valve.
Thus Hiddink after Luis Felipe Scolari and Mourinho part two, and the Roberto Di Matteo / Eddie Newton double-act after bull-in-a-china-shop Andre Villas-Boas.
But neither is realistically a long term option, as at the very highest level, players need more day-to-day drive than that.
Antonio Conte's managerial honours
Comedian Al Murray, in character as affable xenophobe The Pub Landlord, has a recurring gag that – like most good comedy – contains a grain of truth.
“You see, Britain is all about rules,” he says, before asking the audience, “if we had no rules where would we be?”
“France!” is the reply.
Murray then asks: “If we had too many rules where would we be?”
And people shout back: “Germany!”
The joke appeals because it plays on stereotypes developed in our parents and grandparents youth.
But beyond that we all know that in any society, be it a nation of 50 million or a football squad of 24, a balance needs to be found between there being too many, or not enough rules.
Conte, hammer or not, will need to maintain that balance at Chelsea.
He will have to push his players harder than they have been pushed before, but at the same time make them crave for more of the same.
Here again Pirlo has some words that suggest Conte is just the man to do that.
“I have played under a lot of great managers,” said the midfielder.
“But I can say that Conte is a genius. Like all men who possess genius, he is a little mad.
“The man can be a beast, a dressing room when he is angry is one of the most dangerous places you can be.”
Chelsea's players may find this coming season that if they can keep Conte happy, then success will follow very easily.