The former Blues defender has left Burton to replace Lee Clark as the new manager at St Andrews.
Rowett will be bringing three more former Blues players with him from Burton in Kevin Summerfield, Kevin Poole and Mark Sale as part of his coaching staff.
"After the success Gary has achieved at Burton Albion over the last three years it was inevitable that there would be interest from other clubs," Burton chairman Ben Robinson told his club's official website:
"Gary is an ambitious young manager and the offer from one of his former clubs playing Championship football was one he wanted to take.
"We wish him well and thank Gary and his coaching team for what they have done for the club."
Rowett's first match in charge of Blues will be Saturday's Midlands derby against Wolves at Molineux.