From 1927 to 1944, Cordier was a professor at his alma mater Manchester College and chair of the department of history and political science, also teaching at Indiana University extension.

Cordier is noted for convincing Dean Rusk and Ambassador Yakov Malik to meet in the basement of his Great Neck, New York home to discuss how to lessen U.S.–Soviet tensions.

Cordier was considered responsible[2] for facilitating the first US-supported coup against Congo Prime Minister Patrice Lumumba by closing airports and radio stations to him while his opponents had such facilities available to them.

[6] After leaving the United Nations, Cordier joined Columbia University as the Dean of the School of International Affairs (SIA), serving in that role from 1962 to 1972.

The trustees were sufficiently pleased with his work that they gave him the permanent title in 1969; Cordier accepted on the condition that the search for a new president continue.