Luiz informed the club of his decision to leave in May, despite the Gunners being keen on extending his deal for another season.
The defender, who joined from London rivals Chelsea for a fee of £8million in 2019, made 73 appearances for the club but missed the end of the 2020-2021 season through injury.
Real Madrid duo Odegaard and Ceballos return to the LaLiga side following the end of their loan spells.
Odegaard joined the Gunners in January while Ceballos spent two years on loan with the club.
Goalkeeper Ryan, who joined on loan in the winter, will return to parent club Brighton. The shot-stopper made three appearances five-month spell in north London.