"The nightmare is over for the people of Ivory Coast, there is much celebration." he said. "He is now being held in a safe place for the next steps to put him on trial."
Gbagbo, who has held power since 2000 and stubbornly refused to admit defeat in November's presidential election, was detained and taken to his rival's temporary headquarters with his wife Simone and son Michel.
French President Nicolas Sarkozy and Ouattara talked at length on the phone just after Gbagbo's arrest on Monday.
Meanwhile, the security situation in Abidjan is unclear. Some districts are still controlled by Gbagbo loyalists including the downtown business district of Plateau and nearby Cocody.
Troops from France and a UN peacekeeping force have been pounding Gbagbo's forces since Sunday in a bid to destroy the heavy weapons they were reportedly using against civilians.
UN chief Ban Ki-moon confirmed he had ordered Sunday's attack and repeated UN accusations that the Gbagbo camp had used an offer of talks he made last week "to regroup their forces and redeploy heavy weapons".
France on Monday said its military had taken part in the weekend raids at the UN chief's request, but denied reports that its special forces had taken Gbagbo and handed him over to Ouattara's men.
Ouattara said late Sunday he had asked the UN to "neutralise the heavy weapons," and has promised that Gbagbo will face justice for alleged crimes