The accession was marked at a closed-door ceremony at ICC headquarters in The Hague, exactly 90 days after Palestine joined the court's founding Rome Statute.
The Palestinians called on Israel to also join the global court, which was set up in 2002 to try crimes against humanity, war crimes and genocide.
Exasperated after decades of failed negotiations with Israel and no prospect of achieving statehood anytime soon, Palestinians have been waging a campaign for recognition at international bodies including the ICC.
"Palestine seeks justice, not vengeance," foreign minister Riad Malki said after received a symbolic copy of the Rome Statute at the ceremony.
"Israel should join us in becoming a member of the International Criminal Court," Malki said.
Israeli Prime Minister Benjamin Netanyahu "should not be afraid... if Israel has any complaints (against us) they should join and present their case to the ICC."
ICC chief prosecutor Fatou Bensouda in January launched a preliminary investigation into possible war crimes during last year's Gaza war.
The Palestinians have already sent the court documents authorising the prosecutor to investigate alleged crimes in the Palestinian territories since June 2014.
- Preliminary investigation -
About 2,200 Palestinians and 73 Israelis were killed during the 50-day conflict in July and August.
Any probe of alleged Israeli crimes in Gaza would also include an investigation of the firing of rockets and mortars by Hamas militants at civilian areas in Israel.
Despite Israel not being a signatory to the world's only permanent court for the most serious crimes, the tribunal could prosecute Israelis for alleged crimes committed on Palestinian territory.
The ICC would face challenges in arresting Israeli suspects however as it does not have its own police force and relies on the cooperation of member states.
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The Palestinians could in theory now refer a specific situation to the court, such as Jewish settlement building on occupied Palestinian land in the West Bank.
But Malki said Palestine would await the outcome of Bensouda's initial probe.
"We are not in the mood to threaten. We want to wait, we want to give the court ample time to complete their preliminary examination," he said.
Netanyahu has accused the Palestinian unity government -- including Hamas which the Jewish state considers a terrorist organisation -- of "manipulating" the court.
Israel retaliated to Palestine's signing of the Rome Treaty by cutting off millions of dollars in monthly tax payments it collects on behalf of the Ramallah-based Palestinian Authority.
Netanyahu, who was reelected prime minister last month, vowed during his campaign that a Palestinian state would not be established on his watch.
He has since released the frozen funds, which constitute two-thirds of the Palestinian Authority's income, excluding foreign aid.
- Israeli retaliation -
On Tuesday, 26 Americans filed a complaint to the US Attorney General requesting the justice ministry prosecute Hamas leaders for "war crimes".
The 26, some of whom also hold Israeli passports, called for Hamas leaders to be prosecuted for firing rockets at Israel's Ben Gurion airport near Tel Aviv during the 2014 war.
In February, a US jury found the PA and Palestine Liberation Organisation responsible for six attacks which killed dozens of people and ordered them to pay the victims' families more than $650 million (605 million euros) in damages.
Human Rights Watch welcomed the accession of the court's 123 member, slamming Israel and the United States for trying to punish Palestine for joining.
"Governments seeking to penalise Palestine for joining the ICC should immediately end their pressure," said HRW's international justice counsel Balkees Jarrah.
"What's objectionable is the attempts to undermine international justice, not Palestine's decision to join a treaty to which over 100 countries around the world are members."
The Palestinians won observer status at the United Nations in 2012 and according to the Palestinian Authority, around 135 countries have now recognised the state of Palestine.