"The government of Israel has agreed to release the entire cargo to the UN in Gaza, again on the understanding that it is for the UN to determine its appropriate humanitarian use in Gaza."
Serry said he had reason to believe that the "de facto authorities" in Gaza, a reference to the Hamas group that controls the Strip, would allow the UN to determine where the aid went.
Nicole Johnston, Al Jazeera's correspondent in Gaza, said it would take a few days for the aid to reach its destination.
"The main sticking point had been Israel's unwillingness to allow construction material and cement into the Strip, they are usually banned items in Gaza as Israel is afraid of Hamas building bunkers.
"It is important to remember this aid is only a drop in the ocean compared to the needs of Gazans.
"People say that while they need aid, what they really need is for Israel's three-year blockade to be lifted."
Up until Tuesday Hamas had refused to accept Israel's conditions on how much of the aid was allowed in, as a protest against its siege on Gaza.
Israel to discuss blockade
Israel seized 10,000 tonnes of goods from the six-ship flotilla in a bloody raid on May 31, killing nine Turkish activists.
Also on Tuesday, Israeli media reported that the country's security cabinet were to meet to consider the possibility of easing the blockade on the Gaza Strip.
Both the public channel and Channel 10 private TV said that Binyamin Netanyahu, Israel's prime minister, under strong international pressure, had decided to "considerably" ease the blockade and to take steps to that end on Wednesday.
A senior Israeli official, who spoke on condition of anonymity, said only that the 15-member security cabinet would "examine on Wednesday matters related to the Gaza Strip."