Fatou Bensouda said the probe would cover events in the Israeli-occupied West Bank, East Jerusalem and Gaza Strip since 13 June 2014, BBC reported.
Last month, the Hague-based court ruled that it could exercise its criminal jurisdiction over the territories.
Israel rejected Ms Bensouda’s decision, while Palestinian officials praised it.
The ICC has the authority to prosecute those accused of genocide, crimes against humanity and war crimes on the territory of states party to the Rome Statute, its founding treaty.
Israel has never ratified the Rome Statute, but the secretary general of the United Nations accepted the accession of the Palestinians in 2015.
In a statement issued on Wednesday, Ms Bensouda said the chief prosecutor was obliged to act “where a state party has referred a situation to the office of the prosecutor and it is determined that a reasonable basis exists to commence an investigation”.
Ms Bensouda said she had carried out a “painstaking preliminary examination” that lasted close to five years and promised that the investigation would be conducted independently, impartially and objectively, without fear or favour.
“We have no agenda other than to meet our statutory duties under the Rome Statute with professional integrity,” she said, noting that she had declined to investigate the 2010 killing by Israeli troops of 10 Turkish activists on the Gaza-bound ship Mavi Marmara.
“In the current situation, however, there is a reasonable basis to proceed and there are admissible potential cases,” she added.
Ms Bensouda also stressed that the “central concern must be for the victims of crimes, both Palestinian and Israeli, arising from the long cycle of violence and insecurity that has caused deep suffering and despair on all sides”.
Israeli Prime Minister Benjamin Netanyahu said the decision to open an investigation was “the epitome of anti-Semitism and hypocrisy” and promised to reverse it.
“The State of Israel is under attack tonight,” he warned.
“The court set up to prevent the recurrence of the atrocities perpetrated by the Nazis against the Jewish people is now turning against the state of the Jewish people.”
Palestinian Foreign Minister Riyad al-Maliki said: “The crimes committed by the leaders of the Israeli occupation against the Palestinian people – which are ongoing, systematic and widespread – make this investigation necessary and urgent.”
The US-based campaign group Human Rights Watch said the decision “moves Israeli and Palestinian victims of serious crimes one step closer to obtaining a measure of justice that has for too long eluded them”.