After finishing the Slovene language high school in Klagenfurt in 1967, he enrolled in the University of Graz, where he studied law and Slavic philology.

[6] In December 2020, Inzko, with the help of Sonja Karadžić-Jovičević, succeeded in having a plaque honoring convicted war criminal and Srebrenica genocide perpetrator Radovan Karadžić, Sonja's father, removed after threatening Bosnian Serb leader and Presidency member Milorad Dodik with European Union sanctions if the plaque was not removed within six months.

The National Assembly of Republika Srpska refused to withdraw the honors and claimed that Inzko's demand violates human rights.

"[11] This was met with heavy criticism by Bosnian Serb politicians, especially by Milorad Dodik, stating "We [Republika Srpska] are forced to go into dissolution" and repeating many times that the "genocide did not happen.

[13] The chairman of the Presidency of Bosnia and Herzegovina and its Croat member Željko Komšić also praised Inzko for his "brave decision to impose these much necessary changes.

"[14] Internationally, Inzko got support from Croatian Foreign and European Affairs Minister Gordan Grlić-Radman,[15] as well as from the United States Embassy in Sarajevo.