The Swansea attacker has been announced as a San Paolo player by club chief Aurelio De Laurentiis, ending his two-year spell in the Premier League.
The 28-year-old was a revelation at the Liberty Stadium in his opening season in the Premier League, in 2012-13, but was plagued by injury last campaign and only started 15 times as a result.
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The Spaniard has been strongly linked with a move to Serie A this summer - rumors which were solidified when he did not join the club on its preseason tour of the USA - and Swansea confirmed last week that Napoli was in talks over signing Michu.
De Laurentiis finally confirmed the transfer had been completed on Thursday, although details about how much Napoli has paid and the length of the former Rayo Vallecano star's contract remain unknown.
"Welcome to Michu," the Stadio San Paolo chief wrote on his Twitter, with his message being retweeted by the club's official account.
Michu will link up with coach Rafa Benitez, a fellow Spaniard, at Napoli and joins fellow compatriots Jose Callejon and Raul Albiol at the Serie A club, which finished third in the Scudetto race last season.