The England left-back will remain at Stamford Bridge until the end of the 2013-14 season after protracted contract talks finally came to fruition.
Cole is now keen to enjoy further success for Rafa Benitez's side, having won a number of major trophies, including last season's Champions League.
"When you are going through this kind of thing, of course you always want to stay here but it was also in my mind that I could be leaving a club where I have great memories, and have enjoyed great times," Cole told Chelsea's official website.
"I feel I have a good relationship with the people at the club and the fans and it would have been sad if I had had to leave, so I am glad I have signed for one year.
"When I joined Chelsea I just wanted to try to be successful and win trophies and as player you don't really realise how many games you play each season.
"But to play nearly 300 (matches) in total is brilliant for me, and hopefully I'll play some more."
Cole has suffered with ankle problems in the past but he is in rude health at the moment and has paid tribute to the medical staff at the club.
"I feel fit," he added. "Everyone was always saying about my ankle in the past but it has not been an issue.
"I feel healthy and the physios at Chelsea are brilliant, they look after you and there are great facilities.
"It is a tough league and very demanding but I think I can keep going for a few more seasons yet."