A Fox representative confirmed to Deadline.com that the chief White House correspondent would exit next week after 18 years at the network.
No reason was given and Rosen has not publicly spoken about the move.
ABC News President James Goldston said Vargas will leave her co-anchor job at "20/20" in May "to pursue new ventures."
"From co-anchor of 'World News Tonight' to news anchor for 'Good Morning America,' Elizabeth has served in many key roles here and won nearly every award in broadcasting along the way," The Hollywood Reporter quoted Goldston as saying in a memo to staff.
"But we were most proud of her courage and grace in telling her own story about her struggle with anxiety and alcoholism. Her best-selling memoir has helped so many people by raising awareness about the importance of finding treatment for millions who are still struggling. She continues to be an inspiration for us all."
"I am incredibly lucky to work alongside the very best in the business: the producers, editors, writers on this show, and the enormous team working every week to get our show on the air," she wrote.
"I am so very proud of the stories we have told together," Vargas said in her own note to the staff,
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