Giresse - who took over in 2013 - left his post after failing to guide Senegal through the group stages of the recent African showpiece.
However, former midfielder Cisse will take up the position after spending time as part of the nation's coaching setup in recent years.
Cisse made 35 appearances for the Lions of Teranga and was a key fixture in Senegal's run to the World Cup quarter-finals in 2002.
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