Mertens had been managing director since June 2012. According to a Dong spokesperson, his decision to leave was by "mutual agreement".
Bojsen has been working at Dong since 2008. Speaking about the role, she said: "Germany is still one of our most important core markets.
"We have six North Sea projects with a total capacity of 2GW in the planning that we would like to carry out step by step. But the regulatory framework for that needs to be right."
Prior to joining Dong Bojsen worked for 13 years at consuting and engineering company Grontmij.
Dong started developing the 320MW Borkum Riffgrund 1 in the German North Sea in summer, which is due for completion in 2015.