He died at his home in Croatia, reports variety.com.
His death was announced on the website for Festival of Tolerance, which Lustig oversaw as president since 2008.
Lustig was born in Osijek, Yugoslavia, in 1932 to a Croatian Jewish family. He was a prisoner of the Auschwitz and Bergen-Belsen concentration camps during World War II.
Most of his family members were killed during the war, including his father and grandmother, who died in a gas chamber.
Lustig began work in the Yugoslavian film industry in the mid 1950s. He served as location manager for Norman Jewison's "Fiddler on the Roof" in 1971, as an assistant director on Volker Schlöndorff's "The Tin Drum" and as a supervisor on Alan J. Pakula's "Sophie's Choice".
He met Steven Spielberg after he moved to Los Angeles in the late 1980s. He received his first Academy Award for best picture in 1994 as a producer on "Schindler's List," along with Spielberg and Gerald R. Molen.
"It is a long way from Auschwitz to this stage. The dying ones left me the legacy to tell - if I survive - how it was," Lustig said in his emotional acceptance speech.
Seven years later, Lustig won his second Oscar for "Gladiator," alongside David Franzoni and Douglas Wick.
He was also a producer on the films "Hannibal", "Black Hawk Down", "Kingdom of Heaven", "Good Year" and "American Gangster".
Lustig donated his "Schindler's List" Oscar to Yad Vashem, Israel's Holocaust memorial in Jerusalem. He joined Spielberg to set up a project at the Shoah Foundation to record the testimony of more than 50,000 Holocaust survivors.
Lustig was named an honorary citizen of the City of Zagreb this year for his contribution to promoting the values of a democratic society, film art and a culture of understanding.
"Gladiator" star Russell Crowe tweeted about Lustig, saying: "What an amazing life he led. From the horrors of WWII to the glory of two Academy Awards. He said to me once 'you disagree with me a lot, but you're always my friend on the days I need you.' Yes. Much love Branko. Always your friend."
( With inputs from IANS )