The Nahal Oz fuel terminal will allow in some industrial fuel for Gaza's only power plant, cooking gas for the general public and petrol for United Nations operations.
The Erez crossing will open for journalists and humanitarian workers coming into Gaza.
Ayman Mohyeldin, Al Jazeera's correspondent in the Palestinian coastal strip said the amount of supplies allowed into Gaza is of limited quantity and will only probably last for a few days.
This is only the sixth time Israel has allowed limited supplies into Gaza and only the second time Israeli authorities have opened Erez for journalists and aid workers since November 4.
Israel clamped down on aid shipments to the Gaza Strip on November 4, after the Palestinian fighters responded to an Israeli army raid into the territory with a surge in rocket attacks.
Israel's closure of the crossings prompted the United Nations to warn of a looming humanitarian crisis.
A boat carrying activists supporting the Palestinian cause is expected to arrive in Gaza later in the day, having set sail from Cyprus.
The ship - the SS Dignity - has previously sailed to Gaza, carrying humanitarian activists and a doctor.
Lubna Masarwa, the delegation leader, said: "We have no intention of turning around, and so we're confident that we will reach Gaza.
"We are unarmed civilians carrying desperately needed supplies to other unarmed civilians."
Three-quarters of Gaza's 1.5 million Palestinians rely on humanitarian assistance and UN food aid.