Joining the organization could see the Palestinians pursue Israel on war crimes charges.
Israel and the US, neither of whom are ICC members, have opposed the move.
It comes days after the UN Security Council rejected a resolution demanding an end to the Israeli occupation of the Palestinian territories by late 2017.
Delivering the application to the UN headquarters, the Palestinian envoy to the UN, Riyad Mansour, said it was a “significant step”.
“It is an option that we are seeking in order to seek justice for all the victims that have been killed by Israel, the occupying power,” he said.
The ICC could investigate Palestinian leaders too, were the application successful, and the Israeli Prime Minister, Benjamin Netanyahu, has previously said it was them who should be worried.
“It is the Palestinian Authority – which is in a unity government with Hamas, an avowed terrorist organisation that, like ISIS [Islamic State], perpetrates war crimes – that needs to be concerned about the International Criminal Court in the Hague,” he said.
“We expect the ICC to reject the hypocritical request by the Palestinian Authority, which is not a state but an entity linked to a terrorist organisation,” he added.
The US has called the bid “counter-productive”.
‘Qualified to join’
On Wednesday, the Palestinian leader Mahmoud Abbas signed the Rome Statute, the ICC’s founding treaty.
Under the terms of the statute, it will take about 60 days for the Palestinians to join the ICC after they filed the documents.
A UN spokesman said that the Palestinians had submitted documents to join 16 international treaties.
“The documents are being reviewed with a view to determining the appropriate next steps,” he said.
The Palestinians’ chances of joining were improved in 2012 after the UN General Assembly voted to upgrade their status to that of a “non-member observer state”.
ICC chief prosecutor Fatou Bensouda has previously said that the upgrade means Palestine now qualifies to join the Rome Statute.
Based in The Hague, the ICC can prosecute individuals accused of genocide, crimes against humanity and war crimes committed since 1 July 2002, when the Rome Statute came into force.
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