It was widely believed that the left-back would leave Stamford Bridge in the summer, but news broke at the weekend that Cole had signed a new deal with the Blues.
Despite the fact that Frank Lampard has yet to agree fresh terms with the Londoners, Cech believes that Cole extending his stay with Chelsea is a massive boost for the club.
"Ashley's new deal is great news," Cech told the Chelsea website.
"He is still one of the best full-backs in the world and we want players like that to stay at the club as it shows we still have the ambition and motivation to challenge for everything, it's great to see.
"We still have a very young side. The players gain more experience every day, but we have players who like to play and sometimes you need to shut the door and see the game out. The nature of the players we have is to keep on playing, but the important thing is to improve."
Chelsea travel to Swansea City on Wednesday for their Capital One Cup semi-final second leg.