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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'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
