The Jamaica international, who has two years left on his deal at Pride Park, will join the south London club subject to passing a medical and gaining a work permit.
"We've agreed a deal for Davis to come here," Palace boss Neil Warnock told the Croydon Advertiser.
"What I like about Claude is that he knows how to look after himself - he is physically very strong."
Davis was signed by former Derby manager Billy Davies for £3million from Sheffield United in July 2007.
The 30-year-old spent the final three months of last season on loan at Selhurst Park.