Emery was sacked by Arsenal last November. AFP/File/DANIEL LEAL-OLIVAS
The 48-year-old Emery was dismissed by Arsenal last November with the Gunners on a seven-match winless streak, their worst run since 1992.
He led Sevilla to three straight Europa League titles from 2014-16 before winning five major trophies with French giants Paris Saint-Germain.
“Villarreal CF has reached an agreement with Unai Emery for the Basque manager to be Yellows head coach for the next three seasons,” Villarreal said in a statement.
Villarreal parted ways with former player Calleja this week despite him taking the club to a fifth-placed finish in La Liga.
Influential midfielder Santi Cazorla, who has since joined Qatari side Al-Sadd, also left the Estadio de la Ceramica.
Emery reached the Europa League final last season with Arsenal, losing to London rivals Chelsea.
Villarreal are set to return to Europe’s second-tier competition next term.