The 34-year-old had decided to remain in Spain where he was offered a one-year deal at El Madrigal after his contract expired at the end of the season.
But Senna has since spoken to Brendan Rogers to inform him of his decision to stay at Villarreal.
"I decided to accept the proposal of the Villarreal family and I thank Roig for his confidence," said Senna.
"I am very happy to follow at Villarreal."
