P.S. 35 was established in 1907 in the neighborhood of Stapleton. By the middle of the twentieth century, the school was moved to 60 Foote Avenue, in the Grymes Hill neighborhood. Around that time, an adjacent plot of land was acquired by New York City. This less-than-two-acres parcel was transferred to the New York City Department of Parks and Recreation, as well as the New York City Board of Education.
In 1953, when the site had opened as a park, it was called P.S. 35 Playground. At that time, the park was given basketball courts, handball courts, play equipment, and shuffleboard areas. A plaque was erected in the park in 1997 to commemorate the opening of the park.
Since P.S. 35 is known as the Clove Valley School, the adjacent playground's name was changed to Clove Valley Playground in 1986. Ten years later, it was changed yet again-this time to Terrace Playground, a name which has stayed with the park to this day. The reason for this naming was because the park has three terraces within it.
Terrace Playground is bordered to the north by Foote Avenue, to the south by Martha Street, to the east by Howard Ave., and to the west by P.S. 35. Years after having been opened, the park was given benches, bicycle racks, a comfort station, and a sand pit. In later years, it saw basketball courts, dodgeball areas, and kickball areas. These features are still here today. In 1997, the same year the plaque was erected in the park, recreational facilities were renovated and safety equipment was installed.