The 70-year-old succeeds the sacked Frank de Boer and will oversee his first fixture at Selhurst Park on Saturday against Southampton.
Hodgson, who has signed a two-year contract, becomes Palace’s fourth manager in less than ten months. He will work with a side that has lost all four of their Premier League games without scoring and be asked to secure survival at a club that has been fighting relegation in recent years.
He led Fulham and West Brom to safety having been appointed to work with arguably inferior squads from later stages in the season and Souness is so confident in Hodgson’s ability he believes Palace may even avoid a season-long battle against the drop.
“It will see Palace in the Premier League this time next year,” said Souness, an ambassador for the British Heart Foundation.
“His knowledge, being in the situation before, his natural enthusiasm will rub off on the players and it’ll be a steady appointment.
“He knows the English game, the players he’s working with, what’s needed to be successful in the Premier League.
“People in football would look at Palace and think, ‘that’s a squad that shouldn’t be in a relegation battle’ but that’s where they find themselves after four games.
“You’re in it until you get out of it. You don’t want to be down there for too long. Turning up for work is a problem, games are a problem, getting the crowd back onside is a problem. They need to start winning soon.
“You learn from your mistakes. Roy’s been punched on the nose; he’s also been successful, and he’s at an age where he won’t listen to too many people when it’s going badly or going really well.
“Maybe he feels he has to take a job to get England out of his system. If you have a good job somewhere, that doesn’t make you a fabulous manager, and if you’ve one bad job that doesn’t make you a bad manager. Roy’s had the good and bad.”
There has been criticism of Palace’s board, for handing De Boer a three-year contract and then sacking him 77 days later after only five games, and for the club’s chairman Steve Parish, for publicly discussing the team’s performances.
After Sunday’s 1-0 defeat at Burnley he said he believed their hosts had an inferior squad, and 64-year-old former Rangers boss Souness said: “He should concentrate on the business. If he has any concerns, speak to the manager about that behind closed doors. I don’t think it’s helpful when chairmen start talking about football. Speak to your manager; nine times out of ten the coach will let it go in one ear and straight out of the other, because what do chairmen know about football? That should be kept in private.
“[Palace’s board] have to be big enough to hold their hands up and say, ‘we got it wrong [in appointing De Boer]’.
“He wouldn’t have had the very best players. They would have needed longer to grasp what he was trying to change than if he’d gone to Chelsea, Manchester City or Manchester United, where there are better players.”