Though he served as a diplomat in the government of Czechoslovakia, Korbel's Jewish heritage forced him to flee after the Nazi invasion in 1939. Prior to their flight, Körbel and his wife had converted from Judaism to Roman Catholicism. He served as an advisor to Edvard Beneš, the exiled Czech president in London, until the Nazis were defeated. He then returned to Czechoslovakia, receiving a luxurious Prague apartment previously owned by Karl Nebrich, a Bohemian German industrialist expropriated and expelled under the Beneš decrees. Korbel was asked by Beneš to serve as the country's ambassador to Yugoslavia, but was forced to flee again during the Communist coup in 1948.
Korbel was granted political asylum in the United States in 1949. He was hired to teach international politics at the University of Denver, and became the founding Dean of the Graduate School of International Studies.
One of his students was Condoleezza Rice, the first woman appointed National Security Advisor (January 20, 2001) and the first African-American woman appointed Secretary of State (January 26, 2005). His daughter, Madeleine Albright, became the first female Secretary of State, on January 23, 1997 (Rice was the second).
After his death, the University of Denver established the Josef Korbel Humanitarian Award in 2000. Since then, 28 people have received the Josef Korbel Humanitarian Award.
The Graduate School of International Studies at the University of Denver was named the Josef Korbel School of International Studies on May 28, 2008