Israeli airspace has been closed since last week amid spiralling conflict with Iran.
The flights will depart from Tel Aviv airport once Israeli airspace reopens, with the number of flights based on demand.
British nationals in Israel and the Occupied Palestinian Territories are advised to register their presence to receive further guidance on the flights.
Land routes out of Israel remain open, and UK staff are available to support British nationals who have crossed the border, including providing transport to nearby airports.