The troops encountered no resistance as they headed towards the city, where a building housing ancient manuscripts has reportedly been set on fire.
French and Malian troops have been pushing north in their offensive against Islamist rebels.
On Saturday, they seized Gao, the most populous city in northern Mali.
Thousands of people in Gao poured out into the streets to celebrate the arrival of the troops.
Islamists seized the north of the country last year, but have been losing ground since French forces launched an operation earlier this month.
Continue reading the main story
Analysis
Thomas FessyBBC News, Bamako
French troops seem to have been very successful in retaking the major towns that had been occupied by Islamist militants linked to al-Qaeda for months.
Gao was reconquered over the weekend and Timbuktu should be falling within hours. Kidal will be next.
But this rapid advance has mainly been made possible by the fact that most rebel fighters had left their positions in the few days preceding the French-led operations.
Islamist combatants melted away with all their vehicles and weapons into desert hideouts. Hunting them down in this vast region they know better than any army will be much harder.
The French are hoping for a quick deployment of thousands more African forces but without the experience of the terrain and the equipment, these troops will achieve nothing.
This second phase is likely to last months and the French may well be on the frontline longer than they have said in public.
Most militants appear to have fled into desert hideouts, says the BBC’s Thomas Fessy in the capital, Bamako.
The advance comes as African Union (AU) leaders are meeting to discuss sending more troops to Mali.
‘Killed for celebrating’
“We control the airport at Timbuktu,” a senior Malian army officer told AFP. “We did not encounter any resistance.”
French army spokesman Col Thierry Burkhard told the BBC that “substantial airpower” had been used to support about 1,000 French and 200 Malian forces in their offensive against the militants in Timbuktu.
“Overnight, the French have retaken access points to Timbuktu,” he said.
“The terrorist forces have refused all contact with us. We think they have either gone back into Timbuktu to blend in with the local population or they have fled the city into the north of the country.”
Our correspondent says ground forces units and paratroopers have been despatched around Timbuktu and it is believed that these troops are cautiously trying to find a way into the city.
“We are going to liberate Timbuktu with the Malians very shortly,” French Foreign Minister Laurent Fabius said.
Timbuktu Mayor Halle Ousmane Cisse, currently in Bamako, told the BBC that he had very credible accounts of Islamist militants burning ancient manuscripts that have been kept in the desert city for centuries.
“The rebels set fire to the newly-constructed Ahmed Baba Institute built by the South Africans… this happened four days ago,” he is quoted by Reuters news agency as saying.
It was not yet clear how much of the building had been damaged, he said.
Continue reading the main story
Treasures of Timbuktu
$1· Timbuktu was a centre of Islamic learning from the 13th to the 17th Centuries
$1· 700,000 manuscripts survive in public libraries and private collections
$1· Books on religion, law, literature and science
$1· Added to Unesco world heritage list in 1988 for its three mosques and 16 cemeteries and mausoleums
$1· They played a major role in spreading Islam in West Africa; the oldest dates from 1329
$1· Islamists destroyed mausoleums after seizing the city
He said that the homes of several civil servants had been burnt down during the last week and a young man killed for celebrating the approach of the French-led forces.
Once Timbuktu is secured, the French-led troops are expected to focus on the last rebel stronghold, Kidal, near the border with Algeria.
Kidal – home of the head of Ansar Dine, the main militant group in northern Mali – was bombed overnight by French forces, Malian officials say.
Once Kidal is taken, the first phase of the French operation will be over, our correspondent says.
The second phase will be to track down the militants to their desert hideouts, which could prove a much more difficult task, he adds.
Mr Fabius warned that the militants had adopted a “strategy of evasion and some of them could return in the north”.
Col Burkhard told the BBC that Malian and other African troops – not French forces – would be in charge of holding on to cities after they had been recaptured from militant forces.
He said a contingent of African troops was expected to make their way soon to Mali from Niger’s capital, Niamey.
Some troops from Chad have already entered Gao.
French officials said they now had 2,900 troops in Mali, backed by 2,700 African forces in Mali and neighbouring Chad.
The African contingent is expected to be bolstered to 7,900, including 2,200 troops promised by Chad, AP news agency quotes a Nigerian military official, Col Shehu Usman Abdulkadir, as saying.
At an AU meeting in Ethiopia on Sunday, which is continuing on Monday, outgoing AU chairman and Benin’s President Thomas Boni Yayi criticised the slow response of African states to the Malian conflict.
France’s intervention was something “we should have done a long time ago to defend a member country”, he said.