Earlier on Friday, Khan won a secret ballot against three other candidates from Ireland, Italy and Spain. To win the election, a candidate must receive 62 votes out of the total of 123.
At the June 16 start of his term, Khan will replace current ICC prosecutor Fatou Bensouda.
Khan currently serves as the UN Assistant Secretary-General of the United Nations and leads the UN team to probe allegations of war crimes committed by the Islamic State terror group (banned in Russia).
Khan had worked on several high-profile cases in the past, including at the International Criminal Tribunal for the former country of Yugoslavia and the International Criminal Tribunal for Rwanda.