Hodgson, 75, returns to manage his boyhood club for a second stint after Palace sacked Patrick Vieira last week following a run of 12 games without victory.
The former England manager takes over with the Eagles fighting for Premier League survival, sitting three points above the relegation zone with 10 games to go.
Hodgson said: “It is a privilege to be asked to return to the club, which has always meant so much to me, and to be given the important task of turning the team’s fortunes around.
“Our sole objective now is to start winning matches, and to get the points necessary to ensure our Premier League status.”
Palace’s next game is at home to Leicester when the Premier League resumes after the international break on April 1.