The news comes a day after the Eagles parted ways with Frank de Boer after a disastrous start to the new season which has seen them lose their first four Premier League games without scoring a single goal.
Hodgson, 70, has been out of work since leaving his role as England manager following their Euro 2016 exit 14 months ago and arrives at Selhurst Park with a wealth of club experience, having managed Liverpool, Inter Milan and West Bromwich Albion during a 41-year managerial career.
Speaking to the Palace website, Hodgson said: "This is very much the club of my boyhood and I remember in my youth watching the club from the terraces at the Holmesdale Road end which gave me such fond memories. In those days I had dreams of playing for the team, then as a coach you think about coaching the team and a lot has happened in between times.
"It is very rewarding to find myself here now, in different times, as the Palace manager at a club that I have always loved and admired with a huge potential. We are the club of south London, with an enormously large fan base. The ambitions here are realistic and there is an enormous potential for growth and I hope we can achieve our goals.
"I am very excited to be back in club football and it is a long while since I have enjoyed the day to day sessions of training."
Hodgson's first game in charge of his new side will be a home encounter with Southampton this Saturday.