The Selhurst Park club sacked Dutchman Frank de Boer on Monday after their fourth straight Premier League defeat of the season at the weekend and now sit bottom of the standings without a point.
“I hope it’s close. 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,” Hodgson had told Sky earlier.
He become the second oldest active manager in the top four divisions of English football after Birmingham City’s Harry Redknapp.
“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.
The much-travelled Hodgson has been looking for a job since he quit the England post in June 2016 after a shock 2-1 defeat by Iceland in the European Championship last 16 stage in France.
He last managed at club level with Premier League side West Bromwich Albion, leaving the West Midlands club to take up the England job in 2012. He has also been in charge at Blackburn Rovers,Fulham and Liverpool as well as several clubs in Europe.
Hodgson has little prospect of a honeymoon period, with Palace hosting Southampton before playing the top two sides Manchester City and Manchester United away and then champions Chelsea at home in their next four league matches.
Palace dismissed De Boer after they suffered the worst start to an English top-flight campaign for nearly 100 years — failing to win or even score a goal.
The 47-year-old former Ajax Amsterdam player and manager only took charge on June 26 with a three-year contract.
His reign was the shortest in the Premier League era in terms of matches played.