Andersen is already chairman of Lloyds Register Group, deputy chairman of utility and wind developer SSE, and deputy chairman of VKR Holdings, which has interests in solar energy.
Because SSE and Dong have a partnership within wind energy, working together on offshore projects, Andersen will have to resign his position at SSE.
Andersen will assume the chairmanship on 17 July at an extraordinary general meeting. Until then Benny Loft, who already sits on the board, will act as chairman.
In January, Fritz Schur announced that he was to step down as chairman of Dong following the approval of Goldman Sachs' acquisition of a stake in the company.
Schur, who has been in the post for nine years, said that he was leaving as the company was entering into "new chapter" in the lead up to an initial public offering.
"It is a good time to hand over to a successor," he said.
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