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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Edward Bright, from Ripley, Derbyshire, lost his limbs when he was seven and needs help with much of his life.
When he turned 16 and reapplied for a benefit he was told he had to attend a meeting to be assessed.
The Department for Work and Pensions has now said a face-to-face meeting is not necessary.
Edward's family claimed disability living allowance (DLA) on his behalf to help towards the added cost of life as a quad-amputee but when he turned 16 he had to reapply for a personal independence payment (PIP).
The family were horrified to receive a letter calling him to a meeting with an assessor in Derby and threatening to withdraw the money if he did not attend.
His dad Steve said: "He has already been through all the assessments. Nothing has changed [in his situation] in the last seven years; nothing will change, so being called in to interviews every year is pointless.
"People with disabilities have enough appointments anyway. You should reach a level when it's flagged up on the system: no more interviews needed."
Since the family's case featured in the Daily Mirror, the Department of Work and Pensions has admitted the assessment is unnecessary.
"All DLA claimants are invited to apply for the working-age benefit Personal Independence Payment when they turn 16. In this instance a paper-based assessment has been completed and there is no need for a face-to-face assessment.
"We've tried to call the Brights numerous times to make clear there's no need to attend a meeting on Monday. A letter has been sent through the post."

30 October 2013 Last updated at 17:10 GMT
Last month, the government made changes so head teachers can no longer allow absence outside school holidays, unless there are exceptional circumstances.
It's because of concerns that some kids were missing school for family holidays during term time when it's cheaper.
But more than 125,000 people disagree, signing a petition against the move.
The petition says: "All children who have a good attendance record should be allowed the opportunity to enjoy quality time with their parents on an annual holiday of up to 10 days once per year."
But the government says it's giving schools more freedom to set term dates - which could mean parents could book cheaper holidays.
Ricky's got the story.
Sam Allardyce has made versatile Leicester player Jeffrey Schlupp his first signing as Crystal Palace boss.
[NEXT_CONCEPT]
The family of a teenager who lost his arms and legs from meningitis were shocked when told he had to prove he still needed a disability payment.
[NEXT_CONCEPT]
Your next holiday might seem like a long way off but there's a row brewing about when schoolkids in England should be able to take them.