The 24-year-old moves south for a reported £12m, and has signed a four-and-a-half-year contract.
The Ghana international made 24 Premier League appearances in 2015-16 as the Foxes won their first title.
But he has started only one league game this season and has not featured at all since the 5-0 Champions League defeat at Porto on 7 December.
Schlupp, who can play in defence, midfield or attack, was left out of Ghana's squad for the Africa Cup of Nations in Gabon.
He began his career at Leicester - making 150 appearances for the club, scoring 15 goals - and had a loan spell at Brentford during 2010-11.
West Brom boss Tony Pulis had been interested in Schlupp, who joins a Palace side 17th in the Premier League.
The Eagles, one point above the relegation zone, visit West Ham on Saturday, a game Schlupp is available for.
Allardyce said: "He will bring strength and experience to the defence and will be a major asset for the club."
Sunderland manager David Moyes had earlier confirmed the club had rejected a bid from Palace for Netherlands defender Patrick van Aanholt.
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Sam Allardyce has made versatile Leicester player Jeffrey Schlupp his first signing as Crystal Palace boss.