Throughout the night, jubilant crowds remained in central Green Square, previously the scene of nightly pro-Gaddafi demonstrations.
Rebels met little resistance as they swept in from east, south and west.
A rebel spokesman says pro-Gaddafi forces still control 15-20% of Tripoli.
The rebels also said they had captured Col Gaddafi’s son Saif al-Islam, but there is no word of the colonel’s whereabouts.
Tanks emerged from Col Gaddafi’s Bab al-Azizia compound early on Monday morning and began firing, a rebel spokesman said.
Sustained gunfire has been heard in the area.
Western leaders have welcomed the rebel advance and urged Col Gaddafi to go.
Flags torn down
The BBC’s Tripoli correspondent, Rana Jawad, who has been unable to report openly since March, says people in her neighbourhood in eastern Tripoli were woken by the imam at the local mosque singing the national anthem of the pre-Gaddafi monarchy.
There is very much a sense that the end is near and the rebels have achieved what they wanted, our correspondent says.
In Green Square – which is to return to its original name of Martyrs’ Square – rebel supporters tore down the green flags of the Libyan government and trampled on portraits of Colonel Gaddafi.
“Tonight, the momentum against the Gaddafi regime has reached a tipping point. Tripoli is slipping from the grasp of a tyrant,” said US President Barack Obama in a statement.
UK Prime Minister David Cameron, who is cutting short his holiday to chair a meeting of the National Security Council, said it was clear “that the end is near for Gaddafi”.
Mr Cameron said the Libyan leader had “committed appalling crimes against the people of Libya and he must go now to avoid any further suffering for his own people”.
The International Criminal Court (ICC) has issued arrest warrants for Col Gaddafi, his son Saif al-Islam, and the head of the intelligence service, Abdullah al-Sanussi, for crimes against humanity. ICC prosecutor Luis Moreno Ocampo said he had been informed of Saif al-Islam’s arrest.
Another of Col Gaddafi’s sons, Muhammad, was speaking on the phone to al-Jazeera TV when he said the rebels were surrounding his home. Gunfire was heard before the line cut off.
A diplomatic source told the AFP news agency that Col Gaddafi could still be in Bab al-Azizia. He has not been seen in public since May, although he has broadcast audio messages from undisclosed locations.
TV footage showed Libyans kneeling and kissing the ground in gratitude for what some called a “blessed day”.