The 19-year old New Zealand international has signed a month's youth loan as the Blues kick-off their Championship campaign with a trip to Derby County tomorrow.
Wood has already experienced loans with Barnsley and Brighton in recent times and Baggies sporting director Dan Ashworth said there were plenty of clubs looking to get him across the line.
"There's been a lot of interest in Chris from clubs wishing to take him on loan this summer. But we wanted to keep him here for pre-season and preferably a little longer," Ashworth said.
"After his successful loan spell at Brighton, this has been Roy's (Hodgson) first chance to work with Chris and take a proper look at him.
"He's done really well in pre-season but the opportunity to play both league and potentially European matches with Birmingham, who are right on our doorstep, was perfect for all parties.
"Chris Hughton is also a really good coach, so he will be in safe hands."