Daoud Hanania was born into a Greek Orthodox Christian Palestinian family originally hailed from Jerusalem, Palestine. His father, Anastas Hanania, was a lawyer and politician. The Hananias lived in West Jerusalem until 1948. In the early 1950s they permanently moved to Amman, Jordan, where Hanania's father came to hold several cabinet positions in the Jordanian government, including Foreign Minister, Minister of Justice, Minister for Refugees and Minister of Finance. Anastas Hanania was also Jordan's Ambassador to Great Britain from 1960–1966 and a Senator from 1968 to 1989 in Jordan's Upper House of Parliament.