Trinity Mirror said Cox was being replaced as editor of the Scottish daily tabloid by Bruce Waddell, currently editor of the Scottish Sun.
Cox announced earlier this month that the paper had secured an exclusive interview with the Prince, who is set to celebrate his 21st birthday this year. However, St James's Palace has denied the claims.
Prince William's relationship with the press has become increasingly sensitive in recent months. The prince has repeatedly asked to be left alone by the media as interest in his love life has escalated.
He has also signalled that he may pursue postgradute study in the US for a time in order to lead a more normal life.
Sir Christropher Meyer, chairman of the Press Complaints Commission, said yesterday on 'Breakfast with Frost' that Prince William should be left alone to complete his studies at St Andrews University.
Mark Hollinshead, managing director of Daily Record and Sunday Mail, said: "I would like to thank Peter for his contribution and wish him well for the future."
Waddell will be charged with halting the paper's falling circulation, which hit 507,375 in April, down 1.91% on the previous month.
"Bruce has enormous experience in Scotland and has a deep understanding of the marketplace. I am delighted he is joining our team," Hollinshead said.
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