The vastly experienced 61-year-old spent four months as Albion first-team coach during Roy Hodgson's tenure and will leave his role as Arsenal's head of youth coaching to take up his new position on June 1.
Burton will have a major say in the appointment of a new head coach at the West Midlands club following the departure of Pepe Mel on Monday.
The former Watford, Cardiff City and Sheffield Wednesday assistant manager will work closely with Richard Garlick, whose job title will change from sporting & technical director to director of football administration.
Albion chairman Jeremy Peace told the club's official website: "It's great to welcome Terry back to the club. His knowledge and experience of the game is second to none.
"Terry made a lasting impression during his time here two seasons ago and comes highly-recommended for his new role.
"Richard has worked tirelessly as sporting & technical director and remains a key member of the board.
"However, with the responsibilities of the position becoming increasingly wide-ranging, we felt it would be wise to split the role.
"The appointment of Terry, who has vast experience of coaching, developing young players and identifying talent, can only strengthen the club."
Burton will also be responsible for recommending new signings, while both the first team and Academy set-ups will be report to the Londoner.
