Casey was born in Brooklyn, New York on June 7, 1898. In 1915, he entered the US Military Academy at West Point, where his best friend and roommate was Lucius D. Clay. He graduated third in his class, the class of 1918, and was commissioned as a captain. He served at Camp Humphreys as an instructor and a company commander with the 219th Engineers. He served with the US Occupation forces in Germany from 1920 to 1922.
From 1922 to 1926, he was Professor of Military Science & Tactics, at the University of Kansas.
In 1927, he received his first civil works assignment, with the Pittsburgh District, where he directed a flood control survey. He was responsible for construction at Deadman Island Lock and Dam (now the Dashields Lock and Dam) on the Ohio River. His next assignment was with the Rivers and Harbors Section of the Office of the Chief of Engineers, where he was involved in liaison with Congress on civil works. During this time he designed and patented a floating mooring bit for high-lift locks.
In 1933 he won a two-year John R. Freeman fellowship from the American Society of Mechanical Engineers to study hydraulics and civil engineering in Germany. He attended the Technische Hochschule in Berlin, Germany, earning a Doctorate in Engineering.
Returning to the United States in June 1935, Casey was posted to EastPort, Maine as chief of the Engineering Division at the Passamquoddy Tidal Power Project, a New Deal public works project. There, he established a concrete testing laboratory under Charles E. Wuerpel which is now part of the Structures Laboratory at the Waterways Experiment Station at Vicksburg, Mississippi. After the Passamaquoddy project fell through, Casey served with the Boston Engineer District on flood control surveys of the Connecticut River Valley. In 1937, Casey was sent to the Philippines to advise the government of hydropower and flood control.
He returned to Washington, D.C. in 1940 to become chief of the Design and Engineering Section in the Construction Division of the Office of the Quartermaster General, under Brigadier General Brehon B. Somervell. On the afternoon of Thursday, 17 July 1941, Somervell gave Casey a new special project, the design of an office building to house the entire War Department. Over that weekend, Casey and his staff roughed out the design for a five-story, five-sided structure, which would ultimately become the Pentagon, the largest office building in the world.
In September 1941, General Douglas MacArthur requested Casey's services as his chief engineer. Casey arrived in Manila in October, shortly before the outbreak of war with Japan. Casey supervised demolitions as MacArthur's troops retreated to Bataan. Unlke the rest of MacArthur's headquarters, Casey remained on Bataan and did not relocate to Corregidor. However, he joined the rest of MacArthur's staff in their escape from Corregidor by PT boat in March 1942.
As Chief Engineer at MacArthur's GHQ, Southwest Pacific Area (SWPA), Casey faced enormous challenges. Most of New Guinea consisted of mountains and jungle, with very few airstrips, ports or even roads. All of these had to be constructed by engineers of the U.S. Army, Australian Army and Royal Australian Air Force and United States Navy Seabees. Major air and naval bases were constructed at Port Moresby, Milne Bay, Buna, Lae, Nadzab, Finschhafen, Madang, Hollandia, Biak, Morotai, Leyte, and Manila. In the Philippines, Casey served for a time as commander of the Army Service Command (ASCOM), U.S. Sixth Army.
Casey hoped to become Chief of Engineers but was passed over in favor of Lieutenant General Raymond Albert Wheeler. Instead he remained in Japan as MacArthur's Chief Engineer until his retirement in 1949. He was Chairman of the New York City Transit Authority from 1953-55.