Cross was born March 29, 1848, in Troy, New York to George Cross and Lucy Ann Brown. When he was 14, his family moved to Newburyport, Massachusetts where he attended the Putnam Free School, graduating in 1865. He entered the Massachusetts Institute of Technology as a sophomore in 1867 and graduated in 1870 with a Bachelor of Science. Following graduation, he became instructor in physics, assistant professor in 1871, and full professor in 1875. Cross became chair of the MIT physics department in 1877, after the resignation of Edward Pickering.