As the world's first permanent criminal court, the ICC was set up to try individuals for the world's worst atrocities - genocide, war crimes and systematic human rights abuses.
The new board includes Queen Rania of Jordan; Archbishop Desmond Tutu; former Costa Rican President Oscar Arias Sanchez; former Polish Prime Minister Tadeusz Mazowiecki; and Simone Veil, the former French health minister.
The five were elected on Friday during a meeting of delegates from the 91 countries who have ratified the court's statutes.
The monies are to come from financial assets of convicted individuals as well as contributions from governments and advocacy groups.
The court's chief prosecutor, Luis Moreno-Ocampo of Argentina, said he intended to make massacres and atrocities in the eastern Congo region of Ituri the subject of his first investigation.
Yael Danieli, who specialises in traumatic stress during wartime, said the decision to elect candidates of high stature showed how important the plight of victims of "the world's most heinous crimes" was.
"The election will galvanise the conscience of the international community to fulfil its obligations of justice and redress to victims," she said.