Gbagbo, the first head of state to stand trial in The Hague, and his deputy Charles Ble Goude, were both cleared of crimes against humanity in January and released the following month.
"The appeal will demonstrate that the trial chamber committed legal and procedural errors which led to the acquittals of Mr Gbagbo and Mr Ble Goude on all counts," Prosecutor Fatou Bensouda's office said.
Judges had cleared the pair "without properly articulating and consistently applying a clearly defined standard of proof," said Bensouda.
Bensouda said there had been "incorrect and unreasonable assessment," including in relation to December 2010 rapes. He stated those "errors" had made a material difference in the decision to acquit the accused based on a "partially informed decision" prior to a full written assessment of all findings.
The appeal will go before an appeals chamber of five judges.
Ivory Coast's former prime minister Pascal Affi N'Guessan, who heads Gbagbo's Ivorian Popular Front party, condemned the appeal, which comes just months before the country faces a presidential election.
"These are judicial delaying tactics and political doggedness to keep Laurent Gbagbo and Charles Ble Goude as far away from the country as possible to prevent them from participating in Ivory Coast's political life," he told AFP.
'Other inhumane acts'
Georges Armand Ouegnin, the head of a pro-Gbagbo coalition of political parties and civic groups, echoed him.
"I am deeply disappointed but I'm hopeful," he said, adding that the pair "are innocent".
"It's important that they come back to Ivory Coast for national reconciliation," he added.
Belgium agreed to host Gbagbo, 73, after he was released in February under conditions including that he would return to court for any prosecution appeal against his acquittal.
Ble Goude is meanwhile living in the Netherlands under similar conditions.
Gbagbo faced charges on four counts of crimes against humanity over the 2010-2011 bloodshed which following a disputed vote in the West African nation.
Prosecutors said Gbagbo clung to power "by all means" after he was narrowly defeated by his bitter rival -- now president -- Alassane Ouattara in elections in the world's largest cocoa producer.
He and Ble Goude were tried over responsibility for murder, attempted murder, rape, persecution and "other inhumane acts" during five months of violence, both pleading not guilty.
However, judges dismissed the charges, saying that the prosecution "failed to satisfy the burden of proof to the requisite standard."
Against the backdrop of the Gbagbo controversy, Ivory Coast's opposition are trying to mark out common ground ahead of next year's presidential poll in which Ouattara, 77, has yet to confirm he is standing.