Sijbesma, who has spent 20 years on the Managing Board and almost 13 years as CEO, will support a smooth transition until May.
The firm said he would then seek to pursue other business and personal roles.
It added he had steered DSM through a significant transformation, from a bulk chemicals company into one which focuses on nutrition, health and sustainable living.
Over more than a decade, DSM has significantly expanded its nutrition business, divested its non-core bulk chemical activities, and upgraded its materials portfolio.
"Under Feike’s leadership, DSM repositioned itself into the successful science-based company that it is today: purpose-led and performance-driven, putting innovation and sustainability at the heart of the company and its strategy. Today, DSM is a truly global company with a diverse and engaged employee and leadership base, creating value for all stakeholders," the company said in a statement.
Sijbesma added: “It has been a huge privilege to serve DSM for such a long time. I am deeply grateful to our Board, all my DSM colleagues and business partners for working closely together and for their enormous commitment and contribution. I also thank our customers and shareholders for their trust and loyalty.
"And last, but not least, I am humbled for having been given the opportunity to serve society by creating value on three dimensions simultaneously: people, planet and profit. I will announce new engagements at a later moment and remain passionate driving solutions on global topics. I am proud that the Supervisory Board has chosen my Managing Board colleagues Geraldine and Dimitri, as my successors. Their appointment is well deserved and reflects the collaborative nature of our business, and I wish them every success for the future.
The company said the dual CEO model was established after "a thorough process and external benchmarking, including the advice and input from an international search firm".
In conjunction with their Co-CEO roles, Geraldine Matchett will retain her responsibilities as CFO and Dimitri de Vreeze will hold the COO responsibilities.
Matchett will focus on financial management and capital markets communication, capital allocation, talent and culture development, as well as digital strategy and new ways of working.
de Vreeze will focus on operational delivery, customer centricity, driving growth and efficiency as well as innovation and R&D programmes.
Jointly they will be accountable for the performance of the company, strategy and M&A.