The decision grants the Hague-based ICC jurisdiction to open cases as of April 1 on serious crimes committed in the Palestinian territories, including war crimes committed.
Ban notified states that are party to the ICC of the decision late Tuesday, UN spokesperson Stephane Dujarric told AFP.
"The Secretary General has ascertained that the instruments received were in due and proper form before accepting them for deposit," said a UN statement.
Palestinian leader Mahmud Abbas signed requests to join the ICC and 16 other conventions on Wednesday, a day after the Security Council failed to adopt a resolution paving the way to full statehood.
Israel has retaliated against the Palestinians by freezing some $127 million in tax revenue due to the Palestinian Authority.
The United States has criticised the move as counterproductive and is also threatening to withhold aid.
The Palestinians have asked the ICC to look into possible war crimes committed during last year's Gaza war.
Almost 2,200 Palestinians were killed in July and August during the 50-day war in Gaza, including more than 400 children, according to UN estimates.
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