The 62-year-old has been given a three-year contract, having been touted as a possible successor to Fabio Capello should England's dismal World Cup campaign hasten the Italian's exit.
But Hodgson has been warned by former Liverpool striker John Aldridge about the task which lies ahead.
"He's got a massive job on his hands at Liverpool," said Aldridge.
"This is the most important stage in Liverpool's history since Bill Shankly took over with what's happening off the field with the owners and the lack of stability at the club."
With the sale of the club by co-owners Tom Hicks and George Gillett still dragging on and the futures of Fernando Torres, Steven Gerrard and Javier Mascherano still uncertain, Hodgson will have plenty to keep him busy.
However, with the club' first competitive match being the Europa League third round qualifying first leg on July 29 he has little time to dwell on such issues.
Hodgson's appointment has received a mixed response on Merseyside, with many fans wanting a more high-profile name and plenty keen to see the return of former player and manager Kenny Dalglish, who despite being part of the selection process wanted to step back into the hot-seat after a 19-year absence.
Aldridge believes the former Inter Milan and Blackburn boss does have the necessary credentials, having guided Fulham to a runners-up place in the Europa League this season.
"His experience is fantastic with the jobs he's done in Italy and Switzerland (as coach of the national team," he told Sky Sports News.
"He might have had a bad year or two at Blackburn Rovers, but when you've been in the game as long as he has, you are allowed a few mistakes."