Hundreds of tons of food and medical supplies were destroyed when shells hit the warehouse. At least three schools for Palestinian children were attacked during the three weeks of fighting, U.N. officials said.
Israel invaded Gaza a year ago in response to rockets fired over the border at civilian targets.
"With this payment, the United Nations has agreed that the financial issues relating to those incidents referred to in the terms of reference of the Board of Inquiry are concluded," Martin Nesirky, Secretary-General Ban Ki-moon's spokesman, said.
Nesirky said Ban wanted to note Israel's "cooperative approach" during negotiations for compensation.