Boothroyd, who joined the Baggies from Norwich City just last October, is to begin his new role at Elland Road today (Saturday).
“We wish Adrian all the best in his new role at Leeds," Baggies chairman Jeremy Peace told the clubs official website.
“His time with us has been short but positive for the club and the recruitment that has taken place in the youth department during the last few months means we are well positioned to move forward."
Dan Ashworth will take temporary charge of the Albion Youth set-up until a new appointment is made.