Albion have finished second in League One this season and have gained automatic promotion to the Championship for the 2016-17 campaign.
The former Leeds United striker was in charge of Albion from November 2014 until December 2015.
Hasselbaink guided Albion to promotion from League Two, and when he left the Pirelli Stadium, they were at the top of League One.
Congratulations to everybody @burtonalbionfc!!!— Nasser El Khayati (@elkhayati10) May 8, 2016
What an achievement, getting promoted twice in a row! I am happy
Albion finished second in League One with 85 points from 46 matches, just two points behind leaders Wigan Athletic.
QPR finished 12th in the Championship with 60 points from 46 matches, as many as 14 points behind sixth-placed Sheffield Wednesday.