Staley was born in Florida, Montgomery County, New York on December 12, 1840.

He worked at Union College as an instructor in Civil Engineering from 1867-1868, a professor of that subject from 1868-1876, and the Dean of the Faculty from 1876-1886.

Staley also served as an engineer on the building of the Central Pacific Railroad.

In 1886, Staley became the first president of Case School of Applied Science in Cleveland, Ohio, holding the office until 1902.

During and after his tenure, he also served as a professor of Civil Engineering, Political Economy, and Economics.