The former Chelsea midfielder's free transfer arrival at Anfield is seen as a significant coup by manager Roy Hodgson, who only joined the club on July 1 following the departure of Rafael Benitez.
Cole was expected to remain in London with both Arsenal and Tottenham linked with him, but despite the prospect of playing in the Europa League - courtesy of a seventh-placed finish last term- and uncertainty over the future owners of Liverpool he opted to move to Merseyside.
Having won three league titles with Chelsea, the last coming in May, Cole hopes leaving Stamford Bridge will not bring an end to his medal haul.
But he knows that will not be an easy task as Liverpool have not won a championship since 1990, coming closest to ending that drought in 2008/09 when they ran were a close second behind Manchester United.
"The target of a club like this is the number one place," said Cole.
"There was a lot of difference last season but we are starting afresh and we will be doing everything we can.
"When you play for Chelsea it (winning the league) was expected every year.
"When you come here the whole place is willing it to happen. You can feel that energy and I just want to do my best for the club and if that means we can put some pots on the table then that will be great.
"You just look at the history of the place and it is great that I am pulling on the same shirt as people like Kenny Dalglish, John Barnes - great players.
"I am 28 now and coming into my peak years and I want to be at a club where I am on the pitch as much as possible and helping the team to really do something special.
"I need to feel my confidence again, get myself back to my best, but hopefully I can give my best years to this club.
"I wouldn't have come to the club if I didn't think we could do things and I just need time and games and we will all do it together."
Cole may surprisingly make his debut in Thursday's Europa League third round qualifying round tie against Rabotnicki in Macedonia.
Although Hodgson said he was contemplating whether to throw his World Cup stars back into competitive action against the advice of the club's medical staff Cole hinted that he had already made the decision.
"I am looking forward to it, I can't wait for the first game. It is the Europa League game and hopefully I'll get on the pitch," he added.
"I like to get three or four games under my belt before I am firing on all cylinders.
"We've had a chat but I don't like talking about tactics because the manager will want to keep that close to his chest but I'm looking forward to playing.
"Everyone knows I would love to play centrally with Stevie Gerrard but the manager will decide - I'll play anywhere because the club pay my wages and I have respect for my team-mates.
"Whenever I pull on the shirt I will always give 100% but I feel I can get the best out of myself playing a central role and if I am given time to bed in I can go beyond the levels I achieved already."
Having already referenced the club's legends Cole insisted the decision to give him the number 10 shirt initially allocated to fellow new signing Milan Jovanovic, despite being rumoured to be taking the iconic number seven, was not his.
"I left it up to the club. I didn't choose," he said.