Escriba was dismissed by the La Liga side at the weekend following their 4-0 defeat at Getafe, having helped them to just seven points from their opening six games of the season.
In a statement, the club said: "Villarreal have decided to end the contract of Fran Escriba as coach of the first team. The club would like to thank the coach for his work and dedication."
Calleja had been working as a youth coach at Villarreal for the last three years after calling time on his playing career in 2014 and has now been given the main manager's job on a deal running until the end of the current season.
The Spaniard's first game in charge will come on Thursday night when the Yellow Submarine travel to Maccabi Tel Aviv in the Europa League.