Gbagbo, wearing a suit and tie, sat silently in court listening to proceedings through a headset and made no immediate comment. He sometimes waved and smiled to supporters in the public gallery and looked healthy.
Gbagbo, who is charged as an "indirect co-perpetrator" in the violence, insists he is innocent.
He was arrested in Ivory Coast in April 2011 by forces loyal to Ouattara and extradited to The Hague eight months later.
Some 300 supporters demonstrated outside the court Tuesday, chanting "Free Gbagbo!" and insisting that he is their country's rightful ruler and not Ouattara. "The one who lost is controlling the country. That is ridiculous," said Patrice Koute, who traveled from London to The Hague to show his support.
The court's judges have already ruled that they have jurisdiction to hear the case, but a case can be ruled inadmissible if Ivory Coast is investigating or prosecuting Gbagbo for the same alleged offenses.
Ivorian officials say they have charged Gbagbo only with "economic crimes."
The Hague-based tribunal is a court of last resort, which only tries suspects if countries are unwilling or unable to prosecute them.
"Ivory Coast is neither unable nor unwilling to prosecute President Gbagbo," Jacobs said.
Human rights activists welcomed the start of the hearing, but also used the occasion to urge the court to press charges against supporters of Ouattara allegedly involved in months of post-election violence.
"Holding Gbagbo to account is a critical step for victims in (Ivory Coast)," Param-Preet Singh, senior international justice counsel at Human Rights Watch, said in a statement. "But the slow pace of investigations against pro-Ouattara forces feeds the perception that the ICC is going along with victor's justice."