The school is operated by Falkirk Council on behalf of the Education Department of the Scottish Government.

The catchment area, from which the school's pupil population is drawn, comprises Hallglen, Laurieston, St. Margaret's, Victoria and Westquarter primary schools, located in the east of Falkirk itself and in the nearby Lower Braes villages.

[1] The school is named after Sir John de Graham, a leader in the army of William Wallace.

[3] At the time the Public Private Partnership scheme (PFI) project that included the rebuilding of Graeme High was one of the largest in the UK.

As of 2018, the dedicated coach for the young players at Graeme High is Ian Ross.