Mr Turnbull appeared on the cover wearing a blue striped shirt and red striped tie behind the headline "primed minister."
The issue, which will be on sale from Monday, featured an extended interview with Mr Turnbull, The Australian reports.
In it he spoke about a range of topics including the leadership spill and the public's perception of him.
"If people find me persuasive or offensive that's up to them, but I am comfortable in my own skin and I honestly never ask, 'How can I change myself to be more appealing to people?'" he said in the interview.
Asked whether he would have gone for the Liberal leadership had the spill been successful, Mr Turnbull said: "People would have been astonished if I hadn't."
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