Myers, who served as White House press secretary during President Clinton's first term, will begin work at Burbank-based Warner Bros. on Sept. 2, the Los Angeles Times reported.
Fleishman, who had worked at Warner Bros. for nine years, stepped down from her post this week. She oversaw communications for Warner Bros. during a two-year corporate succession race that ended in January 2013 with the announcement that Kevin Tsujihara would succeed Barry Meyer as chief executive and chairman of Hollywood's biggest movie studio.
In the months after the tense bake-off ended, Tsujihara's two rivals for the job, Jeff Robinov and Bruce Rosenblum,departed the studio.
"It was a great run at a wonderful company," Fleishman said in a statement. "I would like to thank everyone at Warner Bros., particularly my exceptional team, for making each day fun and rewarding."
Myers, whose title will be executive vice president of worldwide corporate communications and public affairs, will report to Tsujihara.
“Kevin has shown himself to be an original thinker and innovative leader, and Warner Bros. is the most storied studio in Hollywood," she said in a statement. "I look forward to joining the Warner Bros. team at this exciting and complex time in the entertainment industry.”
Tsujihara said in a statement that Myers would bring "a creative and strategic mindset" to Warner Bros., which is a subsidiary of Time Warner Inc.
"Her engaging and collaborative demeanor paired with her acute understanding of how to engage constituencies will help us strengthen our position as the leading global studio," Tsujihara said.
Myers was the first woman to hold the position of White House press secretary. After departing the White House, she was a contributing editor to Vanity Fair and political analyst, co-hosting the CNBC talk show “Equal Time.”
She currently serves as managing director of Glover Park Group, a strategic communications firm. Myers is relocating from Washington D.C. to Los Angeles for the job.
Myers is married to journalist Todd S. Purdum, a senior writer for Politico and a contributing editor to Vanity Fair.
Before joining the Clinton presidential campaign in 1991, Myers served as press secretary for Dianne Feinstein in her 1990 bid for governor of California.
Until Myers assumes the post, Jim Noonan, Warner Bros.' senior vice president of worldwide strategic promotions and communications, will serve as the interim head of corporate communications.