Cazorla returned to the Spanish club in 2018 after recovering from a tough, career-threatening injury. He continued delivering impressive performances, helping Villarreal to qualify for the Europa League in the 2019-20 season.
The midfielder bid farewell to Villarreal ahead of the team's final game of La Liga against Eibar on Sunday.
The 35-year-old has enjoyed a brilliant third spell at Villarreal after two years of horrendous injuries.
Cazorla previously made 180 appearances over six years for Arsenal and has 81 caps for Spain. He also played for Malaga and Recreativo Huelva after first joining Villarreal as a teenager.
"We have reached an agreement with Santi Cazorla. He will reach Doha soon to complete the formalities and join the team. Welcome to Al-Sadd, Santi!" the Qatari side wrote on its verified Twitter account.