Kluger, who was 92, died in a Rome hospital on new year's eve of complications from bronchitis and was buried on Monday in Rome's Jewish cemetery. He had been suffering from Alzheimer's disease and had been living in a home for the elderly east of the Italian capital.
Kluger and Karol Wojtyla, the future Pope John Paul II, were classmates in the southern Polish city of Wadowice and were friends from first grade through high school.
"The young Karol Wojtyla learned a lot about Judaism from Kluger," said Italian author Gianfranco Svidercoschi, who was an aide to the late pope and wrote a book about the pontiff's friendship with Kluger.
"He had a great influence on the pope's life," Svidercoschi, who wrote about their friendship in the 1993 book "Letter to a Jewish Friend," told Reuters.
"The young Wojtyla visited the Kluger home in Wadowice, helped Jerzy with his studies, particularly Latin, and started a friendship that would influence his relations with Jews for the rest of his life," said Svidercoschi, who was editor of the Vatican newspaper during part of John Paul's pontificate.
They lost track of each other when World War Two broke out with the German invasion of Poland in 1939 and did not see each other again until 1965.
During the war, Kluger was arrested by the Russians and sent to a gulag in Siberia along with his father.
After Germany invaded the Soviet Union, Kluger was freed and joined Polish forces fighting with the Allies in Africa and Europe under General Wladyslaw Anders and took part in the pivotal battle of Monte Cassino south of Rome.
Towards the end of the war, when he discovered that his mother had been killed in the Auschwitz death camp, he decided to stay in Italy. He studied engineering in Turin and later moved to England.
He settled in Italy again in the early 1960s, working for an import-export company and re-connected with Archbishop Karol Wojtyla in 1965 when Wojtyla was in Rome for the Second Vatican Council. Until they met for the first time since 1938, each presumed the other had died in the war.
After Wojtyla became the first non-Italian pope in 455 years in 1978 they intensified their friendship and Kluger helped organize reunions between the pope and classmates from Wadowice either in Rome or during the pontiff's trips to Poland.
Kluger was in Rome's synagogue when Pope John Paul made his historic visit there in 1986 and called Jews "our beloved elder brothers".
When the pope made his first trip to Israel as pontiff in 2000, Kluger was in attendance at the Yad Vashem memorial to the Holocaust.
Their friendship continued right up to the pope's death in 2005.
"The passing of Jerzy Kluger is both a moment of individual sorrow for the loss of another courageous survivor of the Holocaust, as well as symbolic remembrance for the link with Pope John Paul under whom a revolution in the advancement of Catholic-Jewish relations was realized," said Elan Steinberg vice president of the American Gathering of Holocaust Survivors and Their Descendants.
"Their childhood friendship was seared by their shared experience of coming under the Nazi yolk in Poland. There can be no question that John Paul's warmth and gestures to the Jewish people was shaped by his personal witness of Nazi horrors," Steinberg said.