The move had been expected since last summer when manager Garry Monk confirmed that the once-capped Spain international would not play for the Barclays Premier League club again.
But talks over terminating the player's contract had dragged on until now with both parties seeking to find a suitable settlement.
"Both parties have reached a financial agreement over the remainder of the 29-year-old's contract, which ran until the end of this season," said a statement on Swansea's official club website.
"The agreement will allow Michu to become a free agent and assist him to find a new club straight away in order to kick-start his playing career again in January."
Michu proved an instant hit following his £2million move from Rayo Vallecano in July 2012, scoring four times in his first three games and ending the season with 22 goals as Swansea won the Capital One Cup - the club's first major trophy in 101 years.
But Michu's second season at Swansea became a frustrating affair despite the Oviedo-born player being capped by Spain coach Vincente Del Bosque in a World Cup qualifier against Belarus in October 2013.
Injury restricted him to 24 appearances, in which he scored six goals, and his final game for Swansea came in a 1-0 defeat at Hull in April 2014.
Michu joined Napoli on loan the following season but he made only five appearances for the Serie A club as he suffered further ankle misery, and he is expected to make the move back to Spain after his stint in Wales
Source : PA
Source: PA