Fatou Bensouda has spent the past eight years serving as Luis Moreno-Ocampo's deputy
She is taking over from Argentinian Luis Moreno Ocampo, who is stepping down after nearly a decade in office.
The BBC's Anna Holligan says one of Ms Bensouda's earliest priorities will be bringing Saif al-Islam Gaddafi, the son of the late Libyan leader, to justice.
Ms Bensouda will also be overseeing the ICC's first trial of a former head of state, when the Ivory Coast's ex-President Laurent Gbagbo appears in court.
Liberia's former leader, Charles Taylor, was tried by a UN-backed court trying those responsible for the atrocities during Sierra Leone's civil war.
"As I begin my tenure, moving forward in consolidating current practices, the office will continue to forge ahead with its investigations and prosecutions," she said.
Fatou Bensouda at a glance
- Grew up in the Gambian capital, Banjul
- Father was a civil servant
- Studied law in Lagos, Nigeria
- Became The Gambia's first international maritime law expert
- Joined the justice ministry in 1987 as a deputy public prosecutor
- Became Gambian attorney general and justice minister in 1998
- Worked for Tanzania-based International Criminal Tribunal for Rwanda
- Deputy chief prosecutor at the ICC from 2004-2012
- Becomes ICC chief prosecutor June 2012
Ms Bensouda has spent the past eight years serving as Mr Moreno-Ocampo's deputy.
Our correspondent says that although Ms Bensouda is not new to The Hague, her appointment comes at a time when international justice is increasingly in the spotlight.
She is also taking over during a tense time at the ICC - with four members of staff currently being held in detention in Libya.
Our correspondent says Ms Bensouda has a reputation for controlled calm and sensitivity, which may well have helped her win the job.
The fact that all the suspects wanted or currently on trial at the ICC are African has come in for criticism, with the prosecutor's office often accused of unfairly targeting the continent.
It is hoped that because Ms Bensouda is herself an African lawyer, this could help to silence those critics, our reporter says.
In March, Congolese warlord Thomas Lubanga received the first verdict reached by the court since it was set up 10 years ago.
The prosecution team have asked for a 30-year sentence after he was convicted of recruiting and using child soldiers between 2002 and 2003 in the eastern Democratic Republic of Congo.