Moxey’s existing role of Wolves chief executive has been split into two parts.
Thelwell’s promotion from the role of head of football development and recruitment at Molineux forms part of a reorganised structure under the club’s new owners, the Fosun Group.
Laurie Dalrymple, formerly the club’s head of commercial, becomes managing director and is responsible for all off-the-field activities.
Both will report to Wolves director Jeff Shi, who has so far been the public face of Fosun.
Andrea Butti, previously Monaco assistant technical director and Inter Milan press and team manager, becomes team general manager and will report to new head coach Walter Zenga, while Stefano Cusin has been confirmed as head coach.
Wolves kick off their third successive season in the Championship at Rotherham on Saturday.