Bensounda replaces Luis Moreno-Ocampo in a job that has become one of the most prominent in international law over the past decade. She will be tasked with trying to bring to justice alleged war criminals, including Uganda's Joseph Kony, Libya's Seif al-Islam Gadhafi, and Sudanese President Omar al-Bashir.
In an address to the court, Bensouda said she was "humbled" by her appointment and promised to continue pursuing all cases that fall under the court's jurisdiction.
"As I speak, massive crimes continue to be committed in Darfur (Sudan); Joseph Kony and the Lord's Resistance Army's acts of violence continue unabated in central Africa," she said.
"Nothing short of arresting all those against whom warrants have been issued will ensure that justice is done for millions of victims of the crimes committed by these fugitives."
Court President Sang-Hyun Song oversaw Bensouda's acceptance of the prosecutor's duties in a courtroom in a suburb of the Hague, Netherlands.
The International Criminal Court was founded in 2002 as the permanent successor to numerous ad-hoc war crimes tribunals set up over the past two decades such as the U.N. Yugoslav tribunal and the International Criminal Tribunal for Rwanda.
Bensouda has served as deputy prosecutor at the ICC since 2004.
In her address, she said that Moreno-Ocampo set up the prosecutor's office in 2003 with "two staff members .
"I inherit a well-respected and sound functioning office, with almost 300 staff from 80 countries, seven situations under investigation, 14 cases before the chambers, seven preliminary examinations and one verdict."
In March, trial judges handed down the court's first conviction, that of Congolese warlord Thomas Lubanga, for conscripting child soldiers. He awaits sentencing.
In an interview earlier this month, Bensouda responded to several criticisms frequently put forward against the prosecutor and the court, including that it is used as a political tool by Western powers and that all its current cases involve Africa.
"First of all, let me say that yes, I am an African and I am very proud of that," she said.
"But I am a prosecutor for 121 states parties," she said, referring to all the countries that endorse the court.
She said she would investigate any grave crime in any territory that falls under her jurisdiction, and the international court is bound to be criticized both when it intervenes in a conflict and when it doesn't.
When the court intervenes, as it did in indicting Sudan's al-Bashir and Ivory Coast's former President Laurence Gbagbo, it is accused of selective enforcement. But she said prosecutors must act on the basis of the evidence they have.
"Laurence Gbagbo is our first case" in Ivory Coast, she said. "There will be others."
She said the court is also blamed for failing to intervene, as in the U.S.-led invasions of Iraq and Afghanistan, the Palestinian-Israeli conflict and in Syria—areas where it has no jurisdiction.
"Syria is a case in point," she said. "It's not a member of the ICC, we do not have jurisdiction over Syria unless the U.N. Security Council were to refer Syria to us."
Asked whether she would lobby for countries that don't endorse the court, such as the U.S., to join it, she said that would be outside the scope of her job.
She said she was frustrated by the failure to capture Kony, who was indicted in 2005 . His case became broadly known in the U.S. earlier this year after the "Kony2012" video campaign by a human rights group became an Internet sensation.
But "Joseph Kony, even though we have not been able to arrest him all this while, I think the intervention of the ICC has contributed immensely to bringing peace to Northern Uganda," she said.
She said that countries that support the court have a duty to help it carry out arrests.
"The ICC doesn't have an intervention force," she said. "But the police of 121 member states are the police of the ICC. The armies of these countries are the armies of the ICC."
Moreno-Ocampo, who was present Friday for Bensouda's swearing-in, is expected to take a job with FIFA, the international football (soccer) governing body, investigating corruption in the sport.