Ora was born in Pristina, Yugoslavia (present-day Kosovo), to Albanian parents. Her mother, Vera (née Bajraktari), is a psychiatrist and her father, Besnik Sahatçiu, is a pub owner, having previously studied economics. She was born as Rita Sahatçiu ([sahatˈtʃiu]; surname derived from the Turkish word saatçi, which means "watchmaker"), but her parents later added Ora (which means "time" in Albanian) to the family surname so it could be easily pronounced.

Her family left Kosovo for political reasons, because of the persecution of Albanians initiated with the disintegration of Yugoslavia. They relocated to London, England in 1991, when she was a baby. She grew up in Notting Hill, in West London, and attended a performing arts school, Sylvia Young Theatre School.