Gooch, who joined as a part-time batting coach in 2009, informed that the decision was taken after consultation with Cook and Moores.
England's most prolific run-getter, Gooch said, "Alastair informed me that he was in favour of change. Although this was sad news, I respect his and new coach Peter Moores' right to implement this change of direction."
Gooch, England's record run-scorer in Tests with 8,900 runs in 118 matches, steps down ahead of Moores' first game in charge -- an ODI vs Scotland on May 9.
"To be the guy who rang him up to tell him we're looking to freshen up the coaching staff was incredibly tough for me personally. He's a great man," Cook told BBC.
"But we have made the decision which we think will benefit the England cricket team. There has to be some freshening up - otherwise you get stuck in the past," he added.
60-year-old Gooch, meanwhile, still backs Cook to lead England in the near future: "Alastair is the right man to captain England. He commands respect and will always put his body on the line for his country.
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