The versatile forward had been strongly linked with a move away from the Liberty Stadium in recent weeks and did not travel to the United States for the Welsh club's pre-season tour.
And his switch to Serie A has now been confirmed in a deal that Napoli have the option to make permanent should he impress at the Stadio San Paolo.
Michu arrived at Swansea for a fee of £2.2 million from Rayo Vallecano in 2012 and scored 18 Premier League goals in his first season.
However, the 28-year-old endured an injury-plagued 2013-14 campaign, making just 15 top-flight starts.
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