The former Fulham boss was officially unveiled as successor to Rafa Benitez, who left earlier in the summer, on Thursday after he agreed a three-year-deal.
It is hoped that Hodgson's arrival will bring some stability to Liverpool after a terrible 2009/10 campaign, which saw the club finish seventh in the Premier League, while George Gillett and Tom Hicks want to sell their ownership.
Hodgson wants to talk to club captain Steven Gerrard and vice-skipper Carragher in the near future to outline his plans for the future, but the latter is already relishing the prospect of playing for a man who began his managerial career in 1976.
Carragher told Liverpool's official website: "I'm really looking forward to the opportunity of working with Roy Hodgson as he's got such a great reputation in the game and is one of the most experienced managers in world football.
"After this period of uncertainty, his appointment has given us all a lift."