Napoli’s chairman Aurelio De Laurentiis revealed the news via his Twitter account, saying ‘Benvenuto a Michu’ before Swansea confirmed the news.
Michu joined the Welsh club in 2012 for £2million from Rayo Vallecano and impressed during his first season, scoring 22 goals in 43 matches.
However, the 28-year-old endured a frustrating second season in Wales due to injuries - and netted only twice in 15 starts in the Premier League.
The one-cap Spain international scored 28 goals in 63 games in total for the Welsh club.
Napoli, who are managed by Rafa Benitez, finished third in Serie A last term to secure a place in the Champions League play-offs and also won the Coppa Italia for a fifth time.