Shaw has admitted that he is surprised to be going to the tournament, but says that Cole was quick to congratulate him for being picked.
"It was a very tough decision between me and Ashley but it was about form and the best players at this point," The Mirror quotes him as saying.
"I was very surprised though. I have always watched him and admired Ashley. As I was a Chelsea fan when I was younger I used to go to the games with my mates. He was someone I idolised – the way he played his game – and I looked up to him massively.
"It is a really weird feeling to replace someone I have idolised. He was happy for me and congratulated me on Twitter. I wouldn't say I have taken his place but I have gone to the World Cup in front of him."
Shaw made his debut for England during their 1-0 win over Denmark in March.