Hodgson will be the fourth Reds boss Carragher has worked under after playing for Roy Evans, Gerard Houllier and Rafa Benitez.
The Reds' vice-captain believes the appointment of Hodgson will give the club a lift and has backed him to be a success on Merseyside.
"I'm really looking forward to the opportunity of working with Roy Hodgson," said Carragher.
"He's got a great reputation and is one of the most experienced managers in the world.
"After this period of uncertainty, his appointment has given us all a lift."