Robert Ellis Thompson was born on April 5, 1844, in Lurgan, County Armagh, Northern Ireland.

He was an educator. In 1857, he moved with his family to the United States. He graduated from the University of Pennsylvania (B.A., 1865; M.A., 1868) and began teaching there as an instructor in Latin and mathematics in 1868. In 1871, he was promoted to Assistant Professor of Mathematics. He earned his Ph.D. degree from the Hamilton College, New York, in 1879. He was Professor of Social Science at the University of Pennsylvania (1874-1883) and later became John Welsh Centennial Professor of History and English Literature (1883-1893). Thompson also lectured at Harvard and Yale from 1884 to 1887 and at the Princeton Theological Seminary. He was editor of Penn Monthly (1870-1880) and The American (1881-1892). He published Social Science and National Economy in 1875 and served as editor for the first two volumes of the Encyclopedia Americana, a supplement to the 9th edition of the Encyclopaedia Britannica (1883-1885). In 1887, the University of Pennsylvania awarded him an honorary degree of Doctor of Divinity. He also received an honorary degree of LL.D. from Muhlenberg College in 1909. In 1894, he took over the Presidency of the Central High School in Philadelphia, where he remained until his retirement in 1914. He was an outspoken defender of labour unions (1911) and proponent of female suffrage.

In 1874, he married Mary E. Neely (1845–1894). He died on October 19, 1924, in Philadelphia, Pennsylvania.