The clubs have agreed an undisclosed fee for his services, with the Senegal left-back having travelled to London from the Africa Cup of Nations to sign terms before flying home.
He will return to begin training with Palace, who sit 13th in the Premier League, in the coming days.
Souare, 24, graduated from Lille's academy and featured 55 times in Ligue 1, adding league and Coupe de France honours to his CV in the 2010-11 campaign.
Pardew's side, who lost 1-0 at home to Everton on Saturday, return to action at Leicester City next weekend.
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