The Spanish defender completed a medical on Monday and put pen to paper on a three-year deal with the English Premier League side subject to international clearance.
"I'm very happy to be here,'' Flores told the club's website. "I know I am joining a club that has been growing over the last few years and is still ambitious to go even higher.
"Having played in La Liga and Serie A, two great leagues, it's a dream come true to play in the Premier League, one of the best, if not the best, in the world.''
Flores, also known by many as 'Chico', said new Swansea boss Michael Laudrup played a key role in persuading him to leave Genoa and join the Welsh club, having played under him at Mallorca previously.
"He was one of the main reasons I signed,'' Flores said. "He knows me as a person and a player, so I was honoured when the call came.
"I believe the manager will be good for Swansea and they have done extremely well to get him. Swansea's way of playing is the same style as he wants to play the game. He is the right person to take this club forward.
"Being brought up in Spain, I have the same culture of possession and passing football. I like to play from the back, come forward with the ball, and add to the possession game.
"I'm really looking forward to it. I have been studying Swansea on the internet and I know I am joining a club with passionate supporters who are very close to the players.''
Flores began his career as a youth team player with his hometown club, Cadiz CF, in 2005.
Since then, he has gone on to have loan spells with Racing Club and Barcelona B, while moving on permanently to Almeria and then Genoa.
It was with Genoa that he decided to go out on loan to Mallorca to link up with Laudrup, making 33 appearances under the Danish manager.
