Senegal announced the news in a post on Instagram, without giving any details of the length of the 50-year-old Vieira's contract.
Vieira, who was born in the Senegalese capital of Dakar and moved to France with his family when he eight, went on to win the World Cup with Les Bleus in 1998 during a glittering career which took in both Milan giants, Arsenal and Manchester City.
His coaching career has not been anywhere near as successful, however.
Vieira has previously coached New York City FC, Nice, Crystal Palace and Strasbourg.
His last job was in charge of Genoa, but after an initially positive start, he was fired after less than a year with the team in last place in Serie A.
Senegal were eliminated from the World Cup by Belgium despite leading 2-0 with about five minutes of regulation time remaining.
The team also came close to elimination in the group stage after losses to France and Norway.
Thiaw and his technical staff were dismissed less than two weeks later.
Thiaw, 45, was appointed in 2024 and led the West African nation to a disputed continental title in Morocco this year before the victory was overturned by the Confederation of African Football.
Senegal's appeal to the Court of Arbitration for Sport will be heard on October 8.
