The move was marked at a signing ceremony in The Hague that was attended by diplomats and officials from more than 100 countries but not Israel, which is not a member of the court.
Rights groups welcomed the step as a signal that the Palestinian Authority favors the rule of law over violence, but Israel has said it damages peace prospects and will not cooperate with the court.
From April 1, ICC prosecutors will have jurisdiction over all future crimes committed on Palestinian territory or by Palestinian citizens.
The ICC is a court of last resort, handling the most serious crimes when local authorities are unable or unwilling to deal with them.
Israel opposes Palestinian membership in the court, a distant successor of the Nuremberg trials of Nazi war criminals after World War Two, and lobbied unsuccessfully for its western allies to cut funding.