Allardyce was appointed following the sacking of Slaven Bilic, and already announced that long time colleague Sammy Lee would be working as his assistant.
Now, the club have confirmed that Morrison will take up the role of first-team coach alongside Stockdale, having been promoted from a coaching role in the academy.
Stockdale worked alongside Allardyce at Sunderland, and links up with the ex-England boss once again.
Morrison and Stockdale make up the final additions to the coaching staff, with Gary Walsh remaining at the club as goalkeeping coach.
Morrison made 341 appearances for the Baggies during his playing career, scoring 39 times.
Stockdale meanwhile has most recently worked at Hibs, assisting Paul Heckingbottom until the start of November.