He follows Dong chairman Fritz Schur out of the door, after Schur announced in January that he would leave the Danish utility.
In a statement issued by Dong, Brogaard referred to the recent acquisition of a stake in the company by investment bank Goldman Sachs, commenting: "With the capital injection in place, it's the right time to make way for new forces."
This echoes Schur's comments, in which he said the buy-in meant new blood was needed at the company.
Brogaard will stand down on 12 March at the company's ordinary general meeting.
Since 2012, Brogaard has been the chairman of the board of directors of Danish state-owned bank Finansiel Stabilitet.