Alassane Ouattara has called for calm after the arrest of his presidential rival Laurent Gbagbo.
Gbagbo was shown on national television urging his supporters to lay down their weapons, though reports say that firing continued in Abidjan throughout Monday night.
Speaking on his TV channel TCI on Monday evening, Ouattara hailed Gbagbo's capture as "the dawn of a new era of hope" for Côte d'Ivoire.
He has asked his human rights minister to open legal proceedings against Gbagbo, his wife and his supporters, but he insisted that they would be kept safe and ensured a fair trial.
Ouattara urged Ivorians to refrain from violence, and pledged to create a peace and reconciliation commission to investigate the atrocities alleged to have been committed by both sides during four months of post-election conflict.
TCI also showed a message from Laurent Gbagbo, recorded shortly after his arrest.
"I hope that we can stop the fighting and get into the civilian part of the crisis," he said, "and that we end it quickly so the country can go back to normal."
According to RFI's correspondent in Abidjan, Marco Chown Oved, the city remains tense.
On Monday night, he reports, "there was intense movement of French armoured vehicles and helicopters still, trying to move out and pacify certain parts of the city.
"We've heard that from the interior of the country, where Ouattara is very popular, there's a lot of celebration. Equally in the northern reaches of the city that have been effectively under Ouattara's control for a month, there's celebration there as well.
"But in the core of the city, where we've seen the majority of the fighting, people are really too afraid to go out still. There are armed gunmen still roaming the streets, despite the calls for them to put down their weapons, and it's still a very, very dangerous place to go out."
International reactions to Gbagbo's capture
France's government said the end of his decade-long rule should help usher in a new era of prosperity for what once one of Africa's most stable nations.
The European Union called for a return to law and order in Côte d'Ivoire and said it was ready to help bring peace to the country.
US President Barack Obama welcomed Gbagbo's capture and called on militia groups to lay down their arms to boost hopes of a democratic future. US Secretary of State Hillary Clinton said the arrest sent a strong signal to the world's dictators that they cannot ignore the will of their people.
United Nations Secretary General Ban Ki-moon said Gbagbo's departure ended what he described as a devastating chapter for Côte d'Ivoire.
The president of Burkina Faso, Blaise Campaoré, said he regretted that it had taken so long for Gbagbo to be arrested and called for reconciliation.