Israel's military says the three hostages have crossed into Israeli territory.

"A short while ago, accompanied by IDF and ISA forces, the released hostages crossed the border into Israeli territory," the IDF says in a statement.

"The released hostages are currently on their way to an initial reception point in southern Israel, where they will undergo an initial medical assessment."

The Israeli government has now officially confirmed the names of the three hostages who have just been handed over to Red Cross workers from Hamas.

A reminder, earlier, it was only Hamas who had released the names of the hostages - Romi Gonen, 24; Doron Steinbrecher, 31; and Emily Damari, 28.

It adds in the statement: "The Israeli government embraces the three returnees. Their families have been informed by the relevant authorities that they have joined our forces.

"The government, together with all security agencies, will accompany them and their families."

Just moments ago, while the hostage release was happening in Gaza, live footage outside Ofer Prison in the occupied West Bank showed several Red Cross coaches entering the prison grounds to pick up Palestinian prisoners.

It is expected that 90 prisoners will be freed from Israeli prisons today, in exchange for the three Israeli hostages.