The Scotland international links up with former Chelsea and Tottenham manager Antonio Conte in Naples, having previously been linked with moves to Premier League clubs Fulham and Tottenham.
The deal is thought to be worth around PS25.5m and include a 10% sell-on clause.
A lengthy statement from United concluded: "McTominay will be missed by everyone at the club and leaves with our best wishes as he embarks on a new chapter of his career in Italy.
"The switch to Serie A giants Napoli sees him him link up again with former United team-mate Romelu Lukaku, who has finalised a transfer from Chelsea, and play under Antonio Conte.
"Good luck, Scott, arrivederci and thank you for the fabulous memories."
McTominay is a graduate of United's academy and made his debut in 2017, before going on to make 255 appearances for the club, scoring 29 goals in the process.
The 27-year-old won the FA Cup, League Cup and Europa League with his boyhood club but has now departed as part of a significant overhaul under Erik ten Hag this summer.
Ten Hag had earlier this summer spoken of his desire to keep McTominay but the imminent arrival of Manuel Ugarte has increased competition for places at Old Trafford.
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