French Colonel Thierry Burkhard said on Monday that there had been no combat with the Islamist militants who had controlled Timbuktu for nearly 10 months.
The French-led operation had surrounded the town early Monday morning, with ground forces seizing the airport to the south without firing a shot and paratroopers landing to the north with backup from combat helicopters.
"The helicopters have been decisive," Burkhard said.
Residents of the town say the occupiers left several days ago.
The Islamists still retain control of the provincial capital of Kidal further north, and are believed to have a complex system of desert bases including self-constructed caves to which they can escape.
French operations against Islamist militants in Mali began 17 days ago when the insurgents moved closer to the south.
The mayor of Timbuktu, currently in the capital Bamako, said the insurgents had torched his office as well as the Ahmed Baba institute - a library rich with historical documents - as an act of retaliation before they fled late last week from the town.
The institute is one of several libraries in Timbuktu with rare documents dating to the 13th century, and houses more than 20,000 manuscripts.
"It's truly alarming that this has happened," Mayor Ousmane Halle told the Associated Press news agency. "They torched all the important ancient manuscripts. The ancient books of geography and science. It is the history of Timbuktu, of its people."
UNESCO spokesman Roni Amelan said the Paris-based cultural agency was "horrified" by the news of the fire, but was awaiting a full assessment of the damage.
Tuareg rebels first captured Timbuktu in April 2012. Before their occupation, the town was known for its ancient mosques and burial grounds.
Not long after the Tuareg takeover, Islamist militants seized control of the town and destroyed or damaged many historical tombs, saying they contravened their hard-line version of Islam.
dr/mkg (AP, AFP, Reuters)