Salisbury was born at Spring Prairie, Wisconsin, in 1858.

He taught in a village school in Port Washington, Wisconsin, for one year before entering Beloit College as a sophomore in the fall of 1878.

After graduating from Beloit in 1881, he spent one year working for the U.S. Geological Survey as Chamberlin's field assistant, during which time he lived in the Chamberlin household.

After Chamberlin left Beloit in 1882, Salisbury joined the college faculty, becoming an assistant professor in 1882 and full professor and chair of the geology department in 1884, remaining there for several years.

At Chicago he became dean of the Ogden Graduate School of Science in 1899, a position he held at the time of his death in 1922.