Stock market opened with modest gain on Wednesday marking third consecutive session in the upward gain
The 45-year-old, formerly in charge of sports brand Nike's marketing division, will take up his post on Jan. 1, the same day as new chairman and fellow Italian Andrea Gaudewnzi.
Briton Chris Kermode has combined the two roles since 2013 but failed to garner enough support in May from the ATP Player Council - headed by Novak Djokovic - and will stand down at the end of December.
An ATP statement said Calvelli was the "unanimous choice" of the ATP Board of Directors.
"I am delighted and honoured to be appointed as the new CEO of the ATP," said Calvelli. "I have been involved in professional tennis for most of my life and I look forward to bringing my passion and knowledge of the sport into this role.
"It's a very exciting time to be involved with the ATP Tour as we strive to build on the growth of recent years, and I look forward to getting started in January."
Former player Gaudenzi welcomed the appointment. "We share a great passion for the sport and I'm confident our diverse business experiences will serve the Tour well as we work on the future direction of men's professional tennis," he said.
Italy will host the ATP Finals from 2021 in Turin, the city taking over from London which has had great success since 2009 in staging the event featuring the world's top eight players.
Matteo Berrettini made his debut at the elite tournament last month after becoming only the fourth Italian to crack the top 10 of the ATP Rankings since they were established in 1973.
The ATP's NextGen Finals are held in Milan.
Calvelli and Gaudenzi's priority will be to smooth the waters after a turbulent a period of political infighting in men's tennis with one of the main concerns of the players being the distribution of prize money despite big increases.
Balancing the demands of tournament owners and players proved to be a never-ending battle for Kermode.
Stock market opened with modest gain on Wednesday marking third consecutive session in the upward gain
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