The 26-year-old, who scored 15 goals in La Liga last season, came through his medical on Thursday and has put pen to paper on a three-year deal subject to international clearance.
New manager Michael Laudrup's believes capturing a player who had attracted the attentions of Manchester United, Liverpool, Sevilla and Valencia for such a low fee represents great business for Swansea.
He said: "It's a fantastic signing. We are talking about a player who scored 15 goals in the Spanish league last year for a small club who were saved by the bell in the last minute of the last game to avoid relegation.
"He was a big difference for them with his goals. We lost Gylfi Sigurdsson, who played in that position for half a season, so to sign a player like Michu is fantastic for us when you look at the price and quality of the player. It is a bargain."
Laudrup is quite right - what a signing this is for Swansea. Quite how they managed to snap Michu up for such a small amount is beyond me but it's a fantastic bit of business. He should enter the Yahoo game around the 6.00 mark and is a player to keep an eye on.