"The detention unit medical officer confirmed Milan Babic's death shortly after his body was found," the court said in a statement.
"The Dutch authorities were called immediately. After conducting an investigation, they confirmed that the cause of death was suicide," it said.
The president of the International Criminal Tribunal for the former Yugoslavia (ICTY) ordered an internal inquiry after Babic killed himself on Sunday.
In 2004 Babic pleaded guilty to crimes against humanity during the war in Croatia after being indicted by the UN court a year earlier and surrendering.
Before that, in 2002 Babic agreed to testify against his former mentor, former Yugoslav president Slobodan Milosevic.
Babic had been due to finish up two weeks of testimony on Monday in the trial of Milan Martic, another Croatian Serb leader.
"He spent two weeks testifying in a very detailed way and at the start he made clear that he completely accepted his guilt and repeated his guilty plea," said Croatian Goran Jungvirth, who is following the trial for the Institute of War and Peace Reporting (IWPR) in The Hague.
Mr Jungvirth added that Babic was testifying "very calmly, not losing his nerve".
He is not the first UN detainee to commit suicide in the Scheveningen prison. In 1998 another Croatian Serb accused, Slavko Dokmanovic, took his own life.
Babic History
A dentist by trade, Babic became the mayor of the central Croatian town of Knin and started to advocate the creation of an independent Serb state within Croatia.
The town later became a stronghold of separatist Serb rebels during the Croatian war that left 25,000 people dead.
Babic went on to become president of the self-proclaimed Serb republic of Krajina, an area that covered a third of Croatia, from May 1991 until February 15, 1992.
With Milosevic's backing, Babic mobilised and arm rebel Serb fighters, and the so-called ethnic cleansing of Croats and other non-Serb populations in Krajina.
Following his guilty plea, Babic was sentenced to 13 years in prison in June 2004, more than the 11 years demanded by the prosecution.
The judges ruled that Babic had played a much bigger role than his lawyer and the prosecution suggested.