He received his education through the public schools in Youngstown and graduated from Rayen High School.
While enrolled at Western Reserve University he enlisted into the United States Army when the United States entered World War I. He served in the United States. Army Ambulance Service and transported wounded individuals from the Battle of Saint-Mihiel and the Meuse-Argonne Offensive to hospitals. During the First Armistice at Compiègne, Gessaman stayed behind for evacuation duty, then served in Germany with the Army of Occupation. After returning home, he resumed his course work at Western Reserve University towards a law degree.
He was admitted to the Ohio bar in 1919.
After graduating from Reserve Law School in 1920, he worked briefly for the private law firm of F. Stanley Crooks. Afterwards, he worked as the assistant City Attorney for Columbus (1923–1928), assistant Franklin County prosecutor (1928–1931), was elected to the Ohio House of Representatives (1933–1935), and served as majority floor leader while a state legislator in 1935.
During 1935, the Republicans of Columbus selected him as their candidate to run for mayor. Gessaman became the 42nd mayor of Columbus, Ohio, the 38th person to serve in that office, and served Columbus during the Great Depression.
After his defeat for reelection as mayor, he was later elected as a judge to the Franklin County Common Pleas Court in 1943.
He served as judge for 30 years. Two years after his retirement from the Franklin County Common Pleas Court he died on August 20, 1975. He is interred at Union Cemetery in Columbus, Ohio.