Chief Justice Jalal Al-Deen Mohamed Osman told the official Sudan News Agency (SUNA) on Saturday that the court, led by Supreme Court judge Mahmoud Mohamed Saeed Abkam, would begin work immediately.
Osman told SUNA that the court would try cases of killing, injury, rape, looting and property damage.
"There will be no impunity for anyone, whatever their position or status, from punishment for a crime committed," he was quoted as saying.
On Monday, the Netherlands-based international court announced the start of an investigation into alleged war crimes in Darfur, where more than 180,000 people have died and 2 million have been displaced during two years of violence.
Sudan insisted it would not hand over any citizen for trial by the international court, saying it intended to set up its own tribunal to prosecute any crimes.
Human rights groups say Sudan's courts cannot be trusted to investigate crimes committed by the country's leaders.
Darfur's crisis erupted when rebels took up arms against what they saw as years of state neglect and discrimination against Sudanese of African origin.
The government is accused of responding with a counterinsurgency campaign in which the ethnic Arab militias, known as Janjawid, committed wide-scale abuses against ethnic Africans.