He has been at the helm of the Dutch feed company for the past six years.
The reason given for his departure is that he is moving back to Norway with his family after having lived abroad for many years.
Nesse had a long career at Nutreco, having worked there for over 23 years.
The CEO built a solid foundation for growth and gave the company a clear strategic direction for the coming years, said the official statement.
Rob Koremans, who has a background in the pharmaceutical industry, is joining Nutreco in August and Nesse is to hand the CEO baton to him in October.
Koremans is said to have worked in executive positions at Serono, part of the Merck Group, Grünenthal and Sanofi-Aventis. Most recently, he was president and CEO of Global Specialty Medicines and a member of the Executive Committee at Teva Pharmaceutical Industries Ltd.