The 48-year-old former Arsenal goalkeeper played for the Royals for four years.
He was appointed youth academy director in 2000 and has been director of football since 2003.
A West Brom statement said: "He played a key role in the Championship club twice winning promotion to the Premier League in 2006 and 2012."
West Brom have appointed Nicky Hammond as technical director, ending his 20-year association with Reading.