His father Aleksa Popović, originally from Vojvodina, was orphaned during the Hungarian Revolution and was adopted as a three-year-old by the Avakumović family in Belgrade in 1848.

Popović attended the first two grades of lower gymnasium in Kragujevac, and the third and fourth in a private school in Jagodina.

When his older brother Mirko became a substitute teacher at the Užice Gymnasium, Dušan moved in with him and there he attended fifth, sixth and eighth grade.

[1] During his fifth or sixth grade at the Užice Gymnasium, Popović joined the Student group "Progress" (Serbian: Đačka družina "Napredak") in 1901.

Alongside Dimitrije Tucović, he launched the Borba newspaper, which was a fortnightly journal of the SSDP, which was published between 1910 and 1914.

Popović supported the ongoing Russian Revolution, as "the best guarantee for world peace" and the "embryo of a new International".