The La Liga club announced the exchange on their official website, with the fee for the 24 year-old Paulista in the region of £15m.
Meanwhile, the 22 year-old Joel Campbell – who enjoyed a hugely successful World Cup in the summer – joins the Yellow Submarine until the end of the season.
Arsenal still need to secure a work permit for Paulista, who made a total of 19 appearances for Villarreal this season. The signing of the Brazilian centre-back sees Gunners boss Arsene Wenger keeping to his promise of signing a defender in the January transfer window, after the long-serving manager was criticised by sections of the Arsenal support for failing to adequately strengthen the backline in the summer.
Paulista is unavailable to play for Arsenal in their FA Cup fourth round tie against Brighton this weekend, but could make his debut when the Premier League returns next week.
Got any questions? Follow me on Twitter @GruffuddOwen