Sigsbee was born in Albany, New York, and grew up in Washington, D.C. He entered the Naval Academy in 1857 and graduated in 1861, just as the Civil War was beginning. He served on several ships during the war, including the USS Brooklyn, which was part of the Union fleet that blockaded the Confederate capital of Richmond, Virginia.
After the Civil War, Sigsbee served on a variety of ships, including the USS Wyoming, which he commanded during a cruise to the Mediterranean Sea in 1875. He also served as the executive officer of the USS Texas, which was part of the fleet that supported the American intervention in the Mexican Revolution in 1876.
In 1897, Sigsbee was given command of the USS Maine, a new battleship that was assigned to the Atlantic Fleet. The Maine was sent to Havana, Cuba, in January 1898, to protect American citizens during a period of political unrest. On February 15, 1898, the Maine exploded and sank in the harbor, killing 266 of its crew. Sigsbee was one of the few survivors.
The sinking of the Maine caused outrage in the United States and led to the Spanish-American War. Sigsbee was widely praised for his courage and leadership in the aftermath of the disaster. He was promoted to the rank of captain in April 1898 and was given command of the USS St. Louis, which he led in several battles during the war.
After the Spanish-American War, Sigsbee continued to serve in the Navy. He commanded the USS Kentucky, which was part of the fleet that blockaded Cuba during the Spanish-American War. He also served as the governor of Guam from 1900 to 1902.
Sigsbee retired from the Navy in 1907 with the rank of rear admiral. He died in Washington, D.C., in 1923.