Hasselbaink, who ended his playing career at Cardiff in 2008, has previously worked with the coaching staff at Nottingham Forest and spent a year managing Royal Antwerp in the Belgian second division.
“Burton Albion Football Club are delighted to announce Jimmy Floyd Hasselbaink as the club’s new manager,” the club said in a statement on their official Twitter feed.
“Jimmy takes over immediately, and will be assisted by David Oldfield, who was Head of Academy Coaching at MK Dons.”
Burton were left searching for a new manager after Gary Rowett departed to take the reins at struggling Championship side Birmingham on October 27.
Hasselbaink said: “I’m very excited to join Burton Albion and follow in the footsteps of Gary Rowett and Nigel Clough. I can’t wait to get started and I’m delighted to be given the opportunity.
“I’m looking forward to working with the players. Until now they have done really well and I’m looking to take them a step further.”
Hasselbaink becomes only the third black and ethnic minority manager in England’s top four divisions - the others being Huddersfield boss Chris Powell and Carlisle manager Keith Curle.