Occupying 2.4ha (24,000 m2), it is located at the junction of Sturt and Morphett streets in the south-western quarter of the Adelaide city grid.

[6] After the removal of indigenous trees during the city's early colonial settlement, Whitmore Square was replanted in the 1850s and fenced to protect it from animals.

[3] In March 2003, as part of the City of Adelaide's dual naming project in association with the University of Adelaide's project[clarification needed], the square was assigned the name "Ivaritji",[8] to commemorate the last full-blood Kaurna person and speaker of the language, a woman also known as Amelia Taylor, who was the daughter of Ityamai-itpina ("King Rodney").

The square was made a dry zone in 2001, and a nearby strip club converted into live music venue, the Whitmore Hotel.

It pays homage to the Afghan cameleers who lived nearby and worshipped at the Central Adelaide Mosque when not working in the outback.

[15] The City of Adelaide, after community consultation, approved the Whitmore Square/Iparrityi Master Plan at the 11 June 2019 Council meeting.