Droppers was born in Milwaukee, Wisconsin to John and Gertrude Droppers on April 12, 1860. He first married Cora Rand, who died in 1896, and later married Jean Tewkesbury Rand in 1897. From 1898 to 1906, he served as President of the University of South Dakota. In 1912, he was a delegate to the Democratic National Convention. Droppers was appointed by Woodrow Wilson as U.S. Ambassador to Greece and Montenegro from 1914 to 1920. Garrett Droppers died on July 7, 1927 in Williamstown, Massachusetts. He graduated from Harvard University.