"The military battle is over now," he said, adding that 90 percent of Kadhafi's compound at Bab al-Azizya "has been secured" with some pockets of resistance remaining.
Proving that the fight was not yet over, at least five mortar bombs rained down on the complex after dark, sending fighters and an AFP correspondent fleeing the darkened maze of high-walled alleys.
A rebel later told AFP that he thought the defiant attack was launched from the capital's loyalist Abu Slim district.
"We will surround it tomorrow, and God willing we will take it. After that we must take the airport road," fighter Akram said.
"But tonight we celebrate. This is a great victory. I say to all the dictators in the world, stand down, and let people live in freedom."
Akram said that Kadhafi had tried to trick rebels by disguising loyalist fighters as cleaners, who pulled guns on rebels inside the compound.
"We killed them," he said, along with around 40 fighters from Abu Slim. The other loyalists in the compound were all African, he said.
Another rebel, Adel Abdel Fatah, said they had taken 60-70 prisoners during the assault, but had also let many loyalist troops go after they handed in their weapons.
But Akram said that there were many heavy steel doors in the underground part of the complex that they could not yet open.
From early in the day the rebels had launched fierce attack on the strongman's sprawling walled compound in the centre of the capital.
The sky was filled with the sound of heavy and light machine guns, as well as mortars, with the overhead roar of NATO jets.
Even two kilometres (about a mile) away from the fighting, the almost constant whistle of bullets could be heard from the rooftops, as chants of "Allahu Akbar" (God is greatest) blared from mosque minarets.
Then the news broke, first that the rebels had breached the walls, then that the compound covering several hectares (acres) had been captured.
An AFP correspondent at the scene said "they have taken Bab al-Azizya. Completely. It is finished."
"Bab al-Azizya is fully under our control now. Colonel Kadhafi and his sons were not there; there is nobody," Colonel Ahmed Omar Bani said from the rebel bastion of Benghazi.
"No one knows where they are," he added.
The whole city erupted with celebratory gunfire.
There were massive traffic jams as whole families drove around honking their horns and waving the pre-Kadhafi red, black and green flag the rebels have adopted as their standard.
From inside the compound, television footage showed a young rebel climbing on a huge sculpture of a fist gripping an F-111 fighter-bomber-- a symbol of a US attack on the compound in 1986 -- trying to break off a piece of it.
Many people gathered outside the partly destroyed building behind the sculpture that Kadhafi had kept in ruins in defiance of the Americans who had bombed it.
Another rebel proudly brandished a seized rifle with a gold-plated barrel and stock saying, "Kadhafi people killed us with it."
As young men tore up a poster portrait of Kadhafi, others ripped the head off a statue of the dictator and trampled on it.
A rebel official said that "at the same house used by Kadhafi before to describe the Libyan people as rats, today the independence flag is flying on its roof."
Huge numbers of people, some armed, others not, on foot, in cars, in pickup trucks were moving around inside the compound before dark.
Amid reports that ordinary citizens were beginning to stream into the complex, rebel television Al-Ahrar called on people to stay away so that insurgent fighters could mop up inside.
It also urged police in Tripoli to remain at their posts in order to guarantee security, while rebels and locals manned checkpoints, stopping and searching cars looking for Kadhafists and weapons.
An old man with three small children came out of a house. They looked bewildered, as if they had not been out for days.
Women who had been weeping earlier in the day with desperation, were now ululating with joy, as thousands flooded the central Martyrs' Square, formerly Kadhafi's Green Square.
Families and carloads of women drove into the square, some with "Liberation" written in henna on the hands, smiling and screaming "We are free!" after breaking the Ramadan dawn-to-dusk fast with family meals.
Just days ago, the head of the rebels' Benghazi-based National Transitional Council, Mustafa Abdel Jalil, had confidently predicted that he would celebrate the feast of Eid el-Fitr -- which will cap Ramadan next week -- in Tripoli.