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.
"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.
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.
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.