“Welcome, Michu!” film magnate De Laurentiis said in an announcement on Twitter, re-used by the club in a rolling feed on their website together with a photograph.
Italian media reported that Michu, 28, will sign a year-long loan deal.
After the payment of an initial fee of around 1.75 million euros (1.38 million pound), Napoli will have the chance to buy the Spaniard for 7.5 million euros at the end of next season, the reports added.
Michu joined Premier League side Swansea from Spanish club Rayo Vallecano in 2012 and scored 22 goals in his first season as the Welsh club claimed their first major honour by winning the English League Cup.
He struggled with knee and ankle injuries last season, making only 19 league appearances, scoring twice.
Napoli finished third in Serie A last season and are seeking to strengthen their squad for a Champions League campaign and fresh title bid under head coach Rafael Benitez, former manager at Valencia, Liverpool, Inter Milan and Chelsea.
(Reporting by Terry Daley; Editing by Tim Collings)
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