Muir will continue as anchor of "World News" on the weekends and will substitute for Diane Sawyer and report during the week as needed.
"David has a true talent for connecting with our viewers, and his award-winning reporting will now find a new home at '20/20,'" Sherwood said in an email message to ABC News staffers. "I'm delighted he's bringing his ample storytelling skills to Friday nights in prime-time, where Elizabeth and the team are delivering the biggest audience in years."
Sherwood also confirmed Cuomo's departure from ABC News for a new job at CNN.
"For the last 14 years, Chris has been an important voice on every program and platform at ABC News," Sherwood said. "Some see injustice in the world and are simply outraged; Chris simply demands answers. ... Chris has been a unique voice at the anchor desk and a valued colleague and friend. We'll miss his energy, commitment and humor and we wish him the very best in this new venture."