His father, Marcus Melchior, was instrumental in the saving of the Danish Jews in 1943 and became chief rabbi of Denmark in 1947. From 1943 to 1945 Bent Melchior was a refugee in Sweden. At the age of 18 Melchior volunteered as a soldier in the Israeli War of Independence of 1948.
After a period as a teacher in Copenhagen Melchior had his rabbinical education in London, and in 1963 he became rabbi at the synagogue in Copenhagen. When his father died in 1969, he succeeded him as chief rabbi for the Jewish community in Denmark. He has translated the Pentateuch, the Siddur (Jewish prayer book) and other books into Danish as well as writing several books including his autobiography. He is a prolific speaker and writer in the Danish community and media. Bent Melchior is married to Lilian; they have four sons, including Michael Melchior.
Bent Melchior retired from the Rabbinate in 1996. His successor was Bent Lexner. Since retiring Melchior has continued his humanitarian and charitable work in Denmark and abroad.