The Seleka rebels advanced into Bangui after an overnight lull in fighting.
One report said Mr Bozize had fled into neighbouring Democratic Republic of Congo.
The rebels, who have been involved in an on-off rebellion since December, accuse the president of failing to honour a peace deal.
One of the rebel leaders on the ground, Colonel Djouma Narkoyo, was quoted by AFP as saying: “We have taken the presidential palace. Bozize was not there.”
He said the rebels were planning to move on to the national radio station in Bangui where rebel leader Michel Djotodia planned to make a speech.
Intense gunfire was reported as rebels advanced through Bangui.
“The rebels control the town,” said a spokesman for the presidency, Gaston Mackouzangba. “I hope there will not be any reprisals.”
A Paris-based rebel spokesman said the rebel leadership was telling its fighters to restrain from “looting or score-settling”.
An unnamed presidential advisor told Reuters news agency that Mr Bozize had crossed the Oubangi River into DR Congo on Sunday morning.
Former colonial power France has called for an emergency meeting of the UN Security Council, and reportedly sent troops to secure the airport.
On Saturday, French officials warned their nationals in the country to stay at home.
France has some 1,250 troops in CAR.
Mineral resources
The rebels joined a power-sharing government in January after talks brokered by regional leaders to end a rebellion they launched last year.
But the deal quickly collapsed, with the rebels saying their demands, including the release of political prisoners, had not been met.
BBC Africa editor Richard Hamilton says government soldiers have been unable to fend off the rebels because Mr Bozize fears being overthrown in a coup and is therefore wary of having a strong army.
He came to power himself in a military coup in 2003.
CAR, which has a population of about 4.5 million, has been hit by a series of rebellions since independence from France in 1960.
It is one of the poorest countries in Africa, despite its considerable mineral resources.
BBC
