Garrett, a nephew of the Johns Hopkins University School of Medicine benefactor Mary Elizabeth Garrett, was born in Baltimore. He was the grandson of John Work Garrett, a longtime president of the Baltimore and Ohio Railroad, and nephew of the Robert Garrett who was namesake of the Robert Garrett Hospital for Children in West Baltimore. His parents were banker T. Harrison Garrett and Alice Dickinson Whitridge Garrett.
Garrett attended Princeton University, earning his B.S. in 1897. While a student, he was a standout athlete in track and field, and competed in the first modern Olympic Games in Athens in 1896. He won gold medals in discus and shot put, and silver in the broad jump.
From 1899 to 1900, Garrett traveled as part of the American Archaeological Expedition to Syria, an expedition that uncovered thirty-three ancient cities. At the conclusion of the expedition, Garrett returned to Baltimore, where he took graduate courses in economics and history at The Johns Hopkins University before starting work at the Robert Garrett & Sons banking and investment house founded by his great-grandfather. He also competed in the 1900 Paris Olympics, where he earned bronze medals in shot put and standing triple jump.
Garrett was a leader in the development of parks and athletic facilities throughout Baltimore, and served as the city’s first chairman of the Board of Park Commissioners for the Department of Recreation and Parks. In 1910, Garrett participated in the organizational meeting of the Boy Scouts of America held in New York, and in 1911, incorporated the Maryland Council of Boy Scouts of America.
Garrett was chair of the Robert Garrett Fund for the Surgical Treatment of Children, which was established in 1936 by the will of Mary Frick Garrett. He was also chair of the Eudowood Sanatorium. The Robert Garrett Fund and the Eudowood Sanatorium joined with the Harriet Lane Home for Invalid Children to fund development of the Children's Medical and Surgical Center at The Johns Hopkins Hospital, which opened in 1964. Garrett held many directorships during his career, including at the Provident Savings Bank, the Safe Deposit and Trust Co., and the Maryland Trust Co. He served as a trustee of Princeton University, on the governing board of the Baltimore Museum of Art, and as a trustee of the Walters Art Gallery.