While the current building, located at 1901 SW Genesee Street, was opened in 1999, Cooper School enjoys a long history in the community, dating back to 1906, when a group of 70 students, children of steel mill workers, attended classes at Youngstown School in a small building offered by the Seattle Steel Company. A year later, a wooden building—know as Riverside School—was built for the school at the base of Pigeon Hill. As the population of the community grew, the wooden structure was replaced by a brick building 1917, which was designed by Edgar Blair, with a 1929 expansion designed by Floyd Naramore. In 1939, the school was renamed to honor Frank B. Cooper, a former Seattle school superintendent. The historic Youngstown School building, located at 4408 Delridge Way SW, now houses an arts and cultural center. It is listed in the National Register of Historic Places.
The first African American teacher hired to teach in Seattle Public Schools, Thelma Dewitty, worked at Cooper School from 1947 until 1953. The Thelma DeWitty Theater at the Youngstown Cultural Arts Center is named after her.