The club have not won a trophy since 2006 and, after finishing seventh last season, are not even in the Champions League.
But Cole, a free transfer after being released by Chelsea, will added some much-needed creativity to the side and Carragher believes that is just what they need.
"He's a player who's won trophies in the past and who at 28 is probably at his peak age," said the Liverpool vice-captain.
"Hopefully over the next three or four years we'll see the best of Joe Cole.
"He's been a top player all through his career, so if we are going to get the best of him then it's great for Liverpool.
"Hopefully he can win some trophies here over the next three or four years."
Adding another Englishman to the ranks is a bonus but Carragher said nationality was less important than quality and a winning mentality.
"You want the best players here for us to be successful. If you can do that with English players then it's all the better," he added.
"Maybe they feel or understand the club a little bit more. But the most important thing is that Liverpool win trophies, not whether the players are English or foreign."
The centre-back knows from personal experience how difficult Cole is to play against.
He just hopes the England international can now start causing problems for other teams.
"He's a goal-getter and he can play in three different positions. Everyone knows he's one of the most skilful players around," he told club website.
"I would probably say he's the type of skilful player we've needed for a few years now, but he also puts the work in for the team.
"I've seen that with England. He's also a good character, a good lad, so it's a great acquisition."