In a statement on the club website (www.dcfc.co.uk), Derby confirmed that Rowett would take charge of the side for his first match at Nottingham Forest on Saturday.
"I'm naturally thrilled to be appointed as the manager of Derby County and can't wait to get started," Rowett said.
"I feel that I have a special bond with the club having been here as a player. During that time, we tasted success when we were promoted to the Premier League and moved to Pride Park Stadium under Jim Smith.
"Living in the local area, I understand the expectation of the fanbase and it goes without saying that Derby County has fantastic and committed supporters."
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Derby, who are currently 10th in the second tier, parted company with Steve McClaren on Sunday after the former England coach's bid for Premier League promotion slumped five months into the season.
Rams chairman Mel Morris said: "We are delighted to welcome Gary Rowett back to Derby County as our new manager.
"Gary is being tasked with, and has the full responsibility for, leading our redevelopment programme. Gary, of course, played for us for three years during his playing career, lives in Derby and is passionate about our football club."
Derby will visit Rowett's former club Birmingham, who have slipped to 17th under replacement Gianfranco Zola, in a league match on April 8.
(Reporting by Hardik Vyas in Bengaluru; Editing by John O'Brien)
