Coulson, who was editor of News of The World for four years, is said to have taken "ultimate responsibility" for the actions of Royal editor Clive Goodman, who was found guilty on Friday of plotting to intercept hundreds of voicemail messages left by staff at Buckingham Palace, including some from Prince William.
Goodman was sentenced to four months in prison, along with private investigator Glenn Mulcaire, who received a six-month sentence for helping Goodman access 609 private messages left by Royal staff and aides and hacking into 487 voicemail messages between November 2005 and June last year.
It is understood Coulson told senior management at News International of his intentions to step down two weeks ago, but decided to hold off a public announcement until the verdicts on Goodman and Mulcaire, who pleaded guilty, were returned.
In a memo to News of The World staff, Coulson said: "I have decided that the time has come for me to take ultimate responsibility for the events around the Clive Goodman case.
"His actions were entirely wrong and I deeply regret that they happened on my watch. I also feel strongly that when the News of The World call those in public life to account on behalf of its readers, it must have its own house in order."
Myler, who was executive editor of sister News Corporation title the New York Post, takes over from Coulson with immediate effect, having previously been editor of the Daily Mirror in 1994 and the Sunday Mirror in 1998.
Les Hinton, executive chairman of News International, said: "I understand Andy's logic and accept his resignation with great sadness. I am sorry events have led to this. Andy's leadership of the News of The World reached great heights."
In his verdict, Mr Justice Gross described the actions of Goodman and Mulcaire as "serious criminal conduct" and "reprehensible in the extreme".
He said: "It's of very first importance to the fabric of our public life that such intrusive, sustained, criminal conduct should be marked by an immediate loss of liberty."
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