Parish confirmed the news on Twitter, posting the message: "Delighted that @papesouare has just this minute signed for #cpfc . A warm welcome from all of us."
The post was accompanied with a picture of himself and the player, who has recently featured in the Africa Cup of Nations for Senegal.
Souare has made 12 Ligue 1 appearances for Lille this season, nine of which have been as a starter.
He becomes Palace's fourth signing of the January window, following the arrivals of Yaya Sanogo, Shola Ameobi and Jordon Mutch.
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