The Academy, a joint project between Apple and the Federico II University in Naples, will train 600 students in app and software development.
The first 100 students - chosen from 4,174 candidates - began their nine-month course on Thursday. They come from all across Italy, with many from the south, as well as various other countries including as the Netherlands, Lithuania and Madagascar.
Students will learn how to develop apps for iOS devices, and a second group will begin in January.
Apple's vice president of Environment, Policy and Social Initiatives, Lisa Jackson, attended the opening and shared pictures of students gathered round Apple Macs.
"Italy has a long history of innovation and design, and Apple feels at home here," Jackson said.
On Facebook, Italian Prime Minister Matteo Renzi thanked Tim Cook, CEO of the tech company, for investing in Italy, saying: "This is just the beginning."
The Apple Academy opens, as promised with Tim Cook. Naples has a great future ahead of it. If the south restarts, Italy restarts.
Renzi and Cook first made the agreement last January, with the location in the eastern outskirts on Naples chosen in March, so the plan has come together quickly.
The Campania region has invested €100 million in the project and pledged another €30 million, while a further €7 million will be used to provide student scholarships.
"From here the economy can be jump-started," said Naples mayor Luigi De Magistris. "Those who have chosen to stay in Naples can finally not only study here but choose to stay, rather than leaving the city to find jobs."
Indeed, the Academy opened on the same day that a report revealed 40,000 young Italians left the country for opportunities abroad last year, leading Italian President Sergio Mattarella to say "a haemorrhage of talent and skills, with no corresponding return, is harmful".
Not only do Italians of the 'millennial' generation have the highest average level of education, the 'Italians in the World' report noted, but they also suffers from the highest unemployment levels.
And with the many programmes offering study and work opportunities to young people abroad, such as Erasmus+, for this generation "the choice is not so much whether to leave, but whether to stay", the writers added.