The Spanish midfielder was due to decide whether to stay in Spain or make the move to Wales by the end of the week.
Senna told followers on Twitter of his decision to stay at Villarreal instead of joining Swansea this evening, thanking the club's president Fernando Roig for his confidence.
Rough translation of Senna's Twitter post: "I decided to accept the proposal of the Villarreal family and I thank Roig's confidence,
"I am very happy to continue."
A later post said: "The only thing missing are the final details, now my rep is talking to the club."
It brings to an end a saga which has dragged on for over a month, with the most likely outcome always being for Senna to stay in his homeland.
The Swans were keen to add his experience to the Premier League squad but will now have to look elsewhere in a bid to strengthen before the big kick-off.