The 54-year-old will also be tasked with finding a replacement for top scorer Marouane Chamakh, who last week joined Arsenal.
Mali-born Tigana was an influential member of the French team that won the European Championships in 1984 and reached the semi-finals at both the 1982 and 1986 World Cups.
He won 52 caps during his career between 1980 and 1988 and played in five French league-winning teams during a playing career that began at Toulon and ended at Marseille via spells with Lyon and Bordeaux.
The Girondins chairman Jean-Louis Triaud will officially present the new club coach at a news conference on Tuesday.
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