Möbius is one of the most prominent German molecular physicists. He studied physics, chemistry, mathematics, and economics at Freie Universität Berlin. In 1969 he completed the habilitation process in experimental physics, and in 1971 he was appointed a professor in the Department of Physics at Freie Universität. In 2001 Möbius officially retired, but he is still active as a scientist and leads several research projects.

Möbius's main research focus is on molecular physics and biophysics. He used sophisticated magnetic resonance methods for his research. In recent years he has participated in several collaborative research centers, working on the analysis of large biological molecules. He coordinated an interdisciplinary Priority Programme of the Deutsche Forschungsgemeinschaft (DFG) dealing with high-field electron spin resonance (a variant of nuclear magnetic resonance) with participation by 20 working groups in Germany and Israel.

In 2006 Möbius was awarded a Grand Cross 1st Class Order of Merit of the Federal Republic of Germany in recognition of his outstanding scientific work in molecular physics and biophysics and his achievements in the development and expansion of international scientific contacts. Möbius has also received numerous other awards, including the Max Planck Research Award, the Philip Morris Research Award, and the Gold Medal of the International Society of Electron Spin Resonance. In 2009 he was elected a Fellow in the highly regarded International Society of Magnetic Resonance.