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.
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."
