The Englishman, who was once a youth player for Palace, has agreed a two-year deal to succeed Frank de Boer at Selhurst Park.
“This is very much the club of my boyhood and I remember in my youth watching the club from the terraces," Hodgson told cpfc.co.uk.
"We are the club of south London. The ambitions here are realistic and there is an enormous potential for growth and I hope we can achieve our goals."
His last position was as manager of the England national team from 2012-2016.
Hodgson and assistant manager Ray Lewington will take training on Wednesday. His first match will be at home to Southampton on Saturday 16 September, kick-off 12:30 BST.