ABC News President Ben Sherwood also announced Tuesday that David Muir will replace Cuomo on "20/20" alongside Elizabeth Vargas.
Muir will continue to anchor "World News" on weekends and when needed as a fill-in for Diane Sawyer.
Cuomo has worked for ABC News for 14 years.
Cuomo will host a new morning show at CNN, where new boss Jeff Zucker, who recently left ABC as executive producer of Katie Couric's talk show, is moving fast to try to turn around the cable news pioneer that has fallen on hard times.
Network managing editor Mark Whitaker announced he was quitting Tuesday, officially Zucker's seventh day on the job as CNN Worldwide president. Longtime political consultants and commentators James Carville and Mary Matalin also are leaving.
Cuomo is expected to be paired with current evening anchor Erin Burnett in the mornings. CNN said Tuesday it was discussing other job options with Soledad O'Brien, who will be ending her second stint as morning show co-host.
"Chris is an accomplished anchor who is already an established name in morning television," Zucker said. "What I love about Chris is that he is passionate about every story he tells, never forgets about the viewer and represents the type of journalism that makes CNN great."
In addition to the broadcast morning shows, CNN is competing with two distinctive cable news morning programs in Fox News Channel's "Fox & Friends" and MSNBC's "Morning Joe."
Zucker was the "Today" show executive producer as the show began dominating morning television in the mid-1990s, before moving up in the NBC executive suite, and he is expected to work closely in developing the new morning show. He was largely responsible for Matt Lauer and Meredith Vieira getting their jobs at "Today."
Cuomo, who was news anchor at "Good Morning America" from 2006 to 2009, was passed over for George Stephanopoulos as co-host of that show while Jake Tapper, who also recently left ABC, twice didn't get a shot at the anchor job on "This Week," first when Stephanopoulos left and then when he returned to the Sunday show.
Both Cuomo and Tapper will have their own daily programs on CNN, which generally runs third in the ratings behind Fox and MSNBC but improves during big news events.
Cuomo wasn't made available for comment. He said in a statement that "this is a fantastic opportunity to do what I value the most and hopefully to do the work that I do best."
CNN was scooped on the announcement of Cuomo's hiring by the newsman's older brother, New York Gov. Andrew Cuomo, who mentioned it during a radio interview Tuesday morning.
Whitaker came to CNN in 2011 as senior vice president and managing editor and tried to expand CNN's programming, opening a film division and hiring Morgan Spurlock and Anthony Bourdain for weekend shows that haven't started yet.
With Zucker and "his own forceful ideas" about CNN's direction and programming options, Whitaker said the new chief deserved a chance to build his own management team.
The Cajun commentator Carville, a former Bill Clinton political aide, has delivered opinions on CNN since 2002. His wife, Mary Matalin, came on at the end of the Bush administration in 2009.
The Associated Press contributed to this report.