Hodgson, who has been out of management since resigning as England boss after they were knocked out of Euro 2016 by Iceland, said he is delighted to be back in football.
He spent part of last season working as a consultant with Melbourne City.
For Hodgson, born in the south London suburb of Croydon, managing Palace means the Englishman is now in charge of his boyhood side after a managerial career spanning five decades and 15 clubs in eight countries as well as spells in charge of four national teams.
Hodgson resigned from his England post immediately after crashing out of the Euro 2016 knockout stages to Iceland, while Zaha has since chose to play for the Ivory Coast after being overlooked by Hodgson's successors Sam Allardyce and Gareth Southgate. The ambitions here are realistic and there is an enormous potential for growth and I hope we can achieve our goals.
Indeed, several senior players are said to have complained about De Boer's "unnecessarily arrogant" conduct during training, chiefly because the 44-year-old would regularly show them all up by "picking balls out of the sky, swivelling on the spot and pinging shots into the top corner".
Wilfried Zaha's England career ended after two caps, with Roy Hodgson opting against relying on the winger, but the pair are reportedly set to link up again. He has previous experience in the Premier League with Blackburn, Fulham, Liverpool and West Brom. "I can't put that right but I'm very pleased to be back at the highest level with a good football club". "It's a fact of life and it's not my business, it's the business of the club", he said.