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 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 Beastie Boys.
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 percent 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.