The company announced the move Monday.
Cohen, 52, said in a memo to staff that he has "always been an entrepreneur at heart" and that his happiest days have been when he has worked to develop artists.
"As WMG enters its next chapter, I'm ready to begin mine," he said in the memo. "I can't yet announce what I'll be doing next, I can only say that it will be something where I can work my entrepreneurial muscles and partner with artists. That's where my passion has always been."
Cohen was credited with restructuring the division after joining Warner in 2004 following its acquisition from AOL Time Warner by a group led by former CEO Edgar Bronfman Jr.
Cohen was recruited by Bronfman following a stint as chief executive at Universal Music Group's Island Def Jam. Prior to that he co-founded Rush Management with partner Russell Simmons, where they managed artists such as Run DMC and the Beastie Boys.
During Cohen's tenure at Warner, the company had hits with artists such as The Black Keys, Bruno Mars and Cee Lo Green.
Warner Music CEO Stephen Cooper said he understood Cohen's "desire to move on to his next challenge."
With Cohen's departure, the company's senior label executives will report directly to Cooper.
Last year, New York-based Warner Music was taken private by billionaire Len Blavatnik for $1.3 billion.
Cohen owned 3.7 million shares, or about a 2.4 per cent stake in Warner, prior to the acquisition, according to a securities filing. The acquisition would have netted him $30.1 million on his shareholdings, plus $12.7 million for stock options and restricted shares he was due as an executive, the filing said.