Rasmussen will be replaced by AP Moller executive Martin Fruergaard in the first quarter of 2016, a statement from Chilean parent Ultranav said.
Chairman Dag von Appen said Rasmussen had led an important era of expansion, consolidation and adjustment at the company since taking the role in 2008.
Rasmussen tells TradeWinds the process has been long-planned as he approaches his 60th birthday and his contract comes to an end.
