The mountains were originally the home of Yankunytjatjara people. The first European to find them was the English explorer William Gosse in the 1870s. He named them after Anthony Musgrave, the Governor of South Australia at the time. At the start of the 20th century, Yankunytjatjara people began migrating east, setting up camps along the Alberga River and moving into the mission at Ernabella. From 1917, they also began a movement southward to Ooldea. Groups of Pitjantjatjara were forced to move to the Musgrave region because of a long drought in their territory, the Mann and Tomkinson Ranges in the west. Today, most of the families in the communities of Amata and Kaltjiti identify as Pitjantjatjara.