According to a report in the Wall Street Journal, Bewkes will take over the media giant, which owns AOL, HBO, CNN and Warner Brothers, by January 1. This is almost six months before Parsons's contract expires.
Parsons has been under fire recently and investors have been waiting to hear when Bewkes would be confirmed into the CEO's job.
Investors want to see action and Bewkes is viewed as someone who can deliver by revitalising the Time Warner share price and possible breaking up the company.
Last week one analyst called for a break-up of Time Warner and labelled Parsons a "lame duck" chairman and CEO.
"We have simply lost faith/trust in TW's executive management team and board of directors," wrote Pali Research analyst Richard Greenfield.
Time Warner is expected to announce large-scale redundancies before its next earnings update and has come under fire for promising much higher growth at AOL than it actually delivered.
When Parsons stands down he will have been at the top of Time Warner for more than five years. He was named CEO in December 2001 when he was promoted from co-chief operating officer to succeed Gerald Levin.
At the time, his appointment was seen as radical, not least because he is black. One newspaper article hailed the decision as of equal importance to US business as Colin Powell's appointment as the first African-American secretary of state was to US politics.
Parsons is expected to retain the chairman's title.
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