The withdrawal follows the departure of French forces from Mali, Burkina Faso, Niger, Chad and Ivory Coast in recent years.
The French embassy in Dakar announced that facilities and housing in the Marechal and Saint-Exupery districts of the capital had been transferred to Senegalese control.
Others "will be returned according to the jointly agreed schedule", it added, without specifying a timeline.
Senegal gained independence from France in 1960 but has remained one of its former colonial ruler's closest allies in west Africa.
But after its election in 2024, Senegal's new government has promised to treat France as an equal to other foreign partners.
French forces have withdrawn from other African countries and left their last base in Chad at the end of January, after the surprise end to military cooperation agreements between Paris and N'Djamena.
Four other former French colonies -- Niger, Mali, Central African Republic and Burkina Faso -- urged France to withdraw its troops from their territories, and have moved closer to Russia.
The French military presence has similarly decreased in Ivory Coast and Gabon, as part of a restructuring plan in west and central Africa.
At the end of February, France handed over the military base in Ivory Coast that it had occupied for nearly 50 years near the economic capital, Abidjan.
The French base in Djibouti, which houses some 1,500 people, is not part of the reduction. Paris wants to make it a "projection point" for "missions" in Africa, after the withdrawal of its forces from the Sahel.
- Sovereignty -
President Bassirou Diomaye Faye, who swept to power on an agenda of change and national self-sufficiency, announced in November that all French and foreign troops would leave Senegal by the end of 2025.
Faye describes himself as a left-wing pan-Africanist.
"Senegal is an independent, sovereign country and sovereignty does not accommodate the presence of (foreign) military bases in a sovereign country," he said in a speech in December.
France announced last month that it had set up a joint commission with Senegal to organise the arrangements for the withdrawal of French troops and the return of the sites by the end of this year.
The embassy said on Friday that the commission met for the first time on February 28.
"The commission also launched work to overhaul the bilateral defence and security partnership," a statement read.
Local staff working for the French military will lose their jobs on July 1, the troops' commander wrote in a letter to a local labour leader.
French military bases in Dakar and the surrounding area directly employ 162 staff, while between 400 and 500 people work in subcontracted industries.
The French army held a careers forum on Thursday to offer "redeployment opportunities" within local companies for the 162 set to be made redundant.
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