The building was designed by the firms of Outcault, Guenther, Rode & Bonebrake, Schafer, Flynn & Van Dijk, and Dalton, Dalton, Little, and Newport,[2] The building has 32 stories, rises to a height of 419 feet (128 m), 1,007,000 square feet (93,600 m2) of space, and is located at 1240 East 9th Street.

Named after Cleveland's 49th mayor, United States Secretary of Health, Education, and Welfare and Federal appeals judge Anthony J. Celebrezze, the Federal Building is typical of the modern, commercial office buildings of the 1960s.

As Federal agencies were moving in 1967–68, a fire hose on the 25th floor burst and water caused damage.

It is lifted by a base of four recessed rectilinear marble volumes, resting upon a field of rough cut slate and granite.

Construction for the Federal Building began with the demolition of the Old Central Armory and the Cuyahoga County Morgue.

[citation needed] Federal agencies with offices in the building include the Defense Finance and Accounting Service, the Coast Guard Ninth District Command Center, recruiting offices for the Armed Forces, the Small Business Administration, U.S. Department of Veterans Affairs, and the Social Security Administration.