The former Leeds and Chelsea striker has left his role at Burton, who are currently top of League One, and signed a rolling contract at Loftus Road.
Hasselbaink replaces Chris Ramsey, who was sacked a month ago following Rangers’ unconvincing start to the season.
Former Hoops boss Neil Warnock was then appointed interim manager and guided the club to two wins, a draw and a defeat from four games, culminating in Thursday night’s 1-0 victory at Reading.
Hasselbaink has enjoyed a hugely impressive start to his managerial career in England, leading Burton to the League Two title in his first season and leaving them challenging for back-to-back promotions.
The 43-year-old Dutchman takes over a Rangers side lying 11th in the Championship following last season’s relegation.