Hodgson was named as Frank de Boer's replacement four league games into the 2017-18 season. t was a homecoming for the south London-born 70-year-old who began his playing career as a youth team player at Palace but never made the first team.
The South London side dismissed De Boer on Monday following their worst start to an English top-flight campaign for almost 100 years.
"I am very excited to be back in club football", Hodgson said, "and it is a long while since I have enjoyed the day-to-day sessions of training".
Palace will be the fifth club Hodgson has managed in the Premier League and his first since leaving West Brom in 2012, with whom he took his career tally to 216 top-flight matches as a manager in England.
Earlier this year, he held talks with Leicester City as a potential candidate to replace Claudio Ranieri.
Shortly after Palace chairman Steve Parish broke the news on his Twitter feed, the south London club put a statement on their website saying Hodgson had signed a two-year contract.
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Former Palace caretaker-boss Ray Lewington will again link with Hodgson as assistant manager, while a new first-team coach will be announced shortly. The ambitions here are realistic and there is an enormous potential for growth and I hope we can achieve our goals.
"I've always got sympathy for managers who lose their job".
"It's a good day for me, I'm very happy and looking forward to hopefully getting down to work and trying to help us get some points in the league and climb up the table", said Hodgson.
"It's a great opportunity to return to the game I love, at the highest level, and also at a club I always admired, liked and supported as well", he said.
"He didn't offer me the job, he just asked me, 'What are your thoughts?' I told him that at this moment in time, I wouldn't want to go back in".