The Ivory Coast right-back, 28, was a free agent after his Spurs contract was terminated by mutual consent at the end of August.
Unai Emery’s Europa League winners have the option of two further seasons after this one so he could stay until 2024.
Aurier spent four years at Tottenham after arriving from Paris St-Germain for about £23m in August 2017.
Villarreal are 11th in La Liga after taking 11 points from their opening seven games and were beaten by Manchester United last week in the Champions League group stage.
Aurier will join up with his new team following the international break, with the Ivory Coast playing two World Cup qualifiers against Malawi.