The company said it had begun the recruitment process to find a replacement for Eldrup. In the meantime, chief financial officer Carsten Krogsgaard Thomsen will be acting CEO.
Update 14 March - in a statement issued by Dong, the Dong chairman Fritz Schur denied Eldrup's departure is connected to a government audit of the company's accounts. However, he did say there was an investigation over the approval of a number of employee contracts by the former CEO.Schur said: "The decision for Anders Eldrup to step down has nothing to do with the examination by Rigsrevisionen (Audit of the State Accounts), but the Board of Directors has learnt that Anders Eldrup has approved some unusual terms of employment for a few employees in Dong Energy.
"At the present time, the Board of Directors is working on the assumption that only a very small number of employees have these unusual terms of employment. To establish the full facts, the Board of Directors has initiated an independent legal inquiry, whose findings are expected to be available in two weeks.
"As the case involves individuals, the Board was unanimous in its wish to hold off providing further details until further clarification was available".
Under Eldrup's control, Dong has become the world's biggest developer in the offshore wind sector. Writing for Windpower Monthly in 2009, Eldrup pointed out Dong had installed half of all offshore turbines globally.
Earlier this year, Dong reported slightly lower figures for 2011, with earnings before interest, tax, depreciation and amortisation (EBITDA) at DK 13.8 billion Danish crowns ($2.46 billion) from DK 14.1 billion in 2010. However the company warned growth would stall in 2012.
In a statement, Schur said: "Anders Eldrup has made a huge contribution to Dong for 11 years and is handing over a strong, well-run company. I wish him good luck with his new challenges.
He added: "Our strategy and investment programme are sound, so the strategic direction will continue unchanged. We will also maintain our ambitious target to double earnings in 2015 compared with 2009."