McTominay joined United at the age of five and played 178 Premier League matches for the club since making his senior debut in 2017, signed for the Serie A club in a deal worth 30.5 million euros ($33.70 million).
"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," Manchester United said in a statement.
McTominay is Napoli's second major signing from the Premier League this week, with striker Romelu Lukaku joining from Chelsea on Thursday.
McTominay made his final appearance for United when he came on as a late substitute during Saturday's 2-1 loss at Brighton.
Napoli, who got their first league win under manager Antonio Conte when they beat Bologna 3-0 last weekend, host Parma on Saturday.