The deal to hand over Tiran and Sanafir was agreed during a visit to Egypt by Saudi King Salman a year ago. It was backed by Egypt's parliament last week.
It has sparked rare protests in Egypt, with Mr Sisi being accused of "selling" territory in return for Saudi aid.
However, a legal battle over the islands' status continues.
One Egyptian court has annulled the handover decision, while another court has upheld it. The constitutional court is yet to make a final ruling on which institution had the final say.
Last week, parliament backed the deal, saying it had jurisdiction in the matter. The move sparked fresh protests in Cairo.
Mr Sisi has said the islands always belonged to Saudi Arabia and that the Saudis asked Egypt to station troops there in 1950 to protect them.
Opponents accuse Mr Sisi of violating the constitution and handing over the islands to please Saudi Arabia which has backed him financially since he led the military's overthrow of his elected Islamist predecessor, Mohamed Morsi, in 2013.