Burton was recently appointed as WBA football director.
"Terry is someone I've respected as a coach from a distance for many years and I'm looking forward to working closely with him," Irvine said.
"The Hawthorns is a place I have been as a visiting manager and assistant manager, and it is always difficult to get a result.
"The fans are extremely passionate, terrific in getting behind the team, and I'm sure it is a great place to work as a player or a coach.
"I'm extremely excited about the challenge and I'll certainly give it everything I can. I'll work however many hours it takes to make things work."
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