Rössler was born in Berlin, into an academic family: his father, also named Otto Rössler, was an Austrian Nazi and a scholar of Semitic languages who was affiliated with the Ahnenerbe and later held a professorship at the University of Marburg.
Rössler was awarded his MD in 1966. After postdoctoral studies at the Max Planck Institute for Behavioral Physiology in Bavaria, and a visiting appointment at the Center for Theoretical Biology at SUNY-Buffalo, in 1969 he became Professor for Theoretical Biochemistry at the University of Tübingen. In 1994, he became Professor of Chemistry by decree.
Rössler has held visiting positions at the University of Guelph (Mathematics) in Canada, the Center for Nonlinear Studies of the University of California at Los Alamos, the University of Virginia (Chemical Engineering), the Technical University of Denmark (Theoretical Physics), and the Santa Fe Institute (Complexity Research) in New Mexico.
Rössler has authored hundreds of scientific papers in fields as wide-ranging as biogenesis, the origin of language, differentiable automata, chaotic attractors, endophysics, micro relativity, artificial universes, the hypertext encyclopedia, and world-changing technology.
His most heavily cited publication is the 1976 paper in which he studied what is now known as the Rössler attractor, a system of three linked differential equations that exhibit chaotic dynamics. Rössler discovered his system after a series of exchanges with Arthur Winfree as detailed by Letellier & Messager (2010).