Born in Chicago, Illinois, Elliott grew up in North Platte, Nebraska, and studied chemistry at the University of Nebraska–Lincoln, where he received his Bachelor of Science (1895) and Master of Arts (1897) degrees.

[5] Elliott continued his research at the University of Wisconsin–Madison and devised a unique scale to rate teachers' merit and competency.

[6] In a series of studies with Daniel Starch, Elliott showed that a student's assignment can receive a wide variety of grades depending on the teacher and the school.

[7] He also participated in commissions that carried out early school surveys of Boise, New York City, Vermont and Portland, Oregon.

One longer-lasting program of Elliott's committees was the establishment of Wisconsin High School, where the university could observe new teachers.

Elliott and Edward O. Sisson, president of the State University, encouraged professor Louis Levine to conduct a study of Montana's tax system.

The mining industry had a significant influence on the Montana legislature, and Elliott warned Levine that his study could harm state appropriations to the university.

[16] Magazines The New Republic and The Nation, Upton Sinclair's book The Goose-Step, and many newspapers considered this an attack on academic freedom and an example of the dominance of the mining industry in Montana.

[17] A review committee at the university upheld Elliott's decision to fire Levine, but asked the State Board of Education to reinstate the professor and reduce the chancellor's power to dismiss faculty in the future.

In 1935 Elliott hired aviator Amelia Earhart and industrial engineer Lillian Gilbreth as visiting faculty members to find ways to improve the education of women.

[22] Early in his presidency, Elliott changed Purdue's budgeting procedures by hiring its first comptroller and business manager.

Once, when asked to fund a new choir, Elliott shouted, "Never, as long as I am president, will this university spend one damn penny on music on this campus, young man!

[34] Higginbotham sought a meeting with the University President, Edward C. Elliott, to ask permission for the students to sleep in a section of one of the heated dormitories.