The 62-year-old succeeds Pole Henryk Kasperczak, who quit the job soon after a first-round exit from the 2015 CAF Africa Cup of Nations.
Giresse suffered a similar fate in Equatorial Guinea as Senegal failed to make the knockout stage despite starting the tournament among the title favourites.
When first in charge of Mali, he guided them to third at the 2012 Cup of Nations co-hosted by Equatorial Guinea and Gabon.
He fell out with former Newcastle United and Chelsea striker Demba Ba, omitting him from the 2015 Cup of Nations squad.
His first task with Mali will be to prepare for the June start of the 2017 Cup of Nations qualifiers.
Although they never won the Cup of Nations, the Eagles have consistently boxed above their weight, finishing second once, third twice and fourth three times.
Giresse was a key cog in the French 1984 European championship-winning team, starring in a midfield that also included current UEFA president Michel Platini.