[1]: 131 Rebstein attended post-secondary school in Winterthur, and after graduating in 1860, went on to study for a year at Collège de France.

[2] He was awarded his doctorate in 1895 from the Humboldt University of Berlin for his work Bestimmung aller reellen Minimalflächen, die eine Schaar ebener Curven enthalten, denen auf der Gauss'schen Kugel die Meridiane entsprechen.

Throughout his career, Rebstein was appointed as surveying expert for a number of cantons, including Thurgau (1863–1881), St. Gallen (1881–1894), Zürich (1886–1892), and Luzern (1894–1907).

[1]: 132 In 1905 he was awarded an honorary doctorate from the University of Zürich, for "outstanding contributions to actuarial sciences".

[2] Rebstein was a member of the organizing committee for the first meeting of the International Congress of Mathematicians.