The deal could grow to become worth up to €30m (£27m/$33m) with add-ons, with Kean set to earn €3m (£2.75m/$3.3m) a year on Merseyside across a five-year contract.
Kean, who has been capped three times by his country, scored six goals in 13 Serie A appearances last term.
“I was convinced to sign because Everton is a club looking to the future and so am I. I know about the size of the Club. It has big ambition and I will work very hard to help us fulfil what we want to achieve.
“I am used to winning and I want to bring this winning attitude to the team. I hope I will be very good on the field and bring the fans joy.”
Marco Silva's side will be looking to improve upon an eighth-place finish in the Premier League last season and identified the young Italian as a shrewd addition to a club looking to make forward strides.
“A striker was one of our priority signings this summer," Silva said in the wake of Kean's signing.
“Moise is strong, fast, with many good qualities as a striker and he is just 19 years old. He has talent and he is ready to work, ready to improve our squad and gives us different solutions.
“Of course he was at a big club, now he’s come to another big club and is ready to fight for this challenge and to give everything to Everton Football Club.”
Kean becomes the club's fifth summer signing following the arrivals of former Huddersfield goalkeeper Jonas Lossl, Idrissa Gueye's replacement Jean-Philippe Gbamin, Fabian Delph and Andre Gomes after he made his loan move from Barcelona permanent.
Everton's Premier League campaign begins on August 10 with a trip to Crystal Palace.