Abdelhamid Abou Zeid, thought to be 47, was a pillar of the southern realm of al-Qaida in the Islamic Maghreb, or AQIM, responsible for the death of at least two European hostages and a leader of the extremist takeover of the north.
The French military moved into Mali on Jan. 11 to push back militants linked to him and others who had imposed harsh Islamic rule and who are seen as an international terrorist threat.
Abou Zeid was killed in operations in the Adrar des Ifoghas mountains in northern Mali in late February, the statement from Hollande's office said.
One analyst warned that Abou Zeid's death will not significantly weaken AQIM, as some analysts predict, and may in fact lead to greater unity among its factions.
Jean-Paul Rouiller, director of the Geneva Center for Training and Analysis of Terrorism, described AQIM's organization as a set of insulated cells under the larger al-Qaida umbrella, which existed independently of each other.
The region of Mali known in the group's parlance as the "emirate of the Sahara" was divided between units loyal to Abou Zeid and those loyal to his rival, Moktar Belmoktar, the international terrorist who led the attack on the Ain Amenas gas plant that left 36 foreigners dead in Algeria earlier this year.
Chad's military chief has claimed that his troops killed Belmoktar, but France has not confirmed the death and many analysts say they don't believe it.
Rouiller said the likely scenario is that Abou Zeid's longtime associate, Yahya Abou El-Hammam, will take over control of his brigade. For years, Hammam acted as the go-between when Abou Zeid wanted to communicate with Belmoktar, suggesting he likely had a good relationship with Belmoktar.
"Especially if Hammam takes over, there could be a chance for a better coordinated relationship with Moktar Belmoktar," Rouiller said. "In terms of controlling Mali, the death of Abou Zeid could mean more cooperation between the arms of AQIM."
Abou Zeid's brigade, believe to be one of the most violent in al-Qaida's North African franchise, was thought to be holding four French nationals kidnapped two years ago at a uranium mine in Niger. The fate of those hostages, working for French company Areva, was unclear.
Abou Zeid held a Frenchman released in February 2010, and another who was executed that July. He's also been linked to the execution of a British hostage in 2009.
A powerful and shadowy figure, mystery surrounds even his real name. Along with his nom de guerre, Abou Zeid had an alias, Mosab Abdelouadoud, and nicknames, the emir of the south and the little emir, due to his diminutive size. But the Algerian press has raised questions about his legal identity Abid Hamadou or Mohamed Ghedir.
He was viewed as a disciplined radical with close ties to the overall AQIM boss, Abdelmalek Droukdel, who oversees operations from his post in northern Algeria.
Abou Zeid fought with a succession of Islamist insurgency movements trying to topple the Algerian state since 1992. He reportedly joined the brutal, and now defunct, Armed Islamic Group that massacred whole villages in northern Algeria, then joined the Salafist Group for Call and Combat that morphed into al-Qaida in the Islamic Maghreb in 2006.
An Algerian court tried him in absentia in January 2012, convicting him of belonging to an international terrorist group and sentencing him to life in prison.
In the Sahara, Abou Zeid was known to be more brutal toward hostages than Belmoktar, who generally allowed foreigners in his care to receive medicine when needed.
Rouiller says that an analysis done by his center of proof-of-life videos released by AQIM suggests that Hammam and another commander are just as brutal as Abou Zeid was.
Associated Press writers Elaine Ganley in Paris and Rukmini Callimachi in Dakar, Senegal contributed to this report.