The 29-year-old joined the club from Rayo Vallecano in 2012 and scored 22 goals in all competitions in his first season at the Liberty Stadium.
However, Michu gradually fell out of favour in Wales and joined Napoli on loan last season, though he made just six appearances for the Italian club.
Michu returned to the Swans in the summer, but failed to make a single appearance under Garry Monk, and has now become a free agent as he goes in search of a new club, with the two parties reaching a financial agreement over the remainder of his deal.
Swansea extended their goodwill to Michu in a statement on their website, writing: “Everyone at Swansea City would like to thank Michu for his services to the club, and wish him well for the future.”