Möbius entered the University of Leipzig (Leipzig, University of) in 1809 and soon decided to concentrate on mathematics, astronomy, and physics. From 1813 to 1814 he studied theoretical astronomy under Carl Friedrich Gauss (Gauss, Carl Friedrich) at the University of Göttingen (Göttingen, University of). He then studied mathematics at the University of Halle (Halle-Wittenberg, Martin Luther University of) before he obtained a position as a professor of astronomy at Leipzig in 1816. From 1818 to 1821 Möbius supervised the construction of the university's observatory, and in 1848 he was appointed its director.

Möbius's reputation as a theoretical astronomer was established with the publication of his doctoral thesis, De Computandis Occultationibus Fixarum per Planetas (1815; “Concerning the Calculation of the Occultations of the Planets”). Die Hauptsätze der Astronomie (1836; “The Principles of Astronomy”) and Die Elemente der Mechanik des Himmels (1843; “The Elements of Celestial Mechanics”) are among his other purely astronomical publications.

Möbius's mathematical papers are chiefly geometric; in many of them he developed and applied the methods laid down in his Der barycentrische Calkul (1827; “The Calculus of Centres of Gravity”). In this work he introduced homogeneous coordinates (essentially, the extension of coordinates to include a “point at infinity”) into analytic geometry and also dealt with geometric transformations, in particular projective transformations that later played an essential part in the systematic development of projective geometry. In the Lehrbuch der Statik (1837; “Textbook on Statics”) Möbius gave a geometric treatment of statics, a branch of mechanics concerned with the forces acting on static bodies such as buildings, bridges, and dams.

Möbius was a pioneer in topology. In a memoir of 1865 he discussed the properties of one-sided surfaces, including the Möbius strip produced by giving a narrow strip of material a half-twist before attaching its ends together. Möbius discovered this surface in 1858. The German mathematician Johann Benedict Listing had discovered it a few months earlier, but he did not publish his discovery until 1861. Möbius's Gesammelten Werke, 4 vol. (“Collected Works”), appeared in 1885–87.