The 28-year-old signed for Liverpool on a free transfer on Monday.
“It’s great news and it is a message that Liverpool mean business,” Carragher told the club’s official website.
“We have signed a top international player who has been really important for Chelsea.
“A lot of clubs wanted to sign him but it is a real coup that he has chosen to come here and you have got to give the manager and the board a pat on the back for convincing him to come here.
“Every supporter that I have spoken to is absolutely delighted and all the players are the same – it’s given everyone a boost, just at the right time.
“It has been a long summer and we have been in a transitional period but now the World Cup is out of the way, we can start to look forward again.
“The fact we have got him has given everyone a boost around the city.
“It’s good news again and, hopefully, there will be more to come. It’s the kind of signing that we needed to make.”