"We felt it's time to freshen things up and move on," BBC Sport quotes Cook as saying. "For me, to still have him in my corner, go back to him, talk cricket, work on my game like I've always done, but we need to thank him for his hard work.
"A lot of the players have a great relationship with him, on a one-to-one basis as well, not just me. I hope those guys will feel free to go and work with Goochy because we all know the work he does is outstanding."
Gooch became full-time batting coach with England in 2011.