O'Donnell made the announcement onstage with The View's co-creator, Barbara Walters.
Earlier, ABC officials declined comment on the prospect of O'Donnell's hiring, which was first reported on TV's Extra.
Friday's edition of The View, which is usually broadcast live, was taped, because its cast and crew are in Los Angeles for the Daytime Emmys ceremony.
A source told PEOPLE that several of those who work on The View had no idea that O'Donnell was coming aboard.
The Rosie O'Donnell Show debuted in 1996 and was an instant hit, earning its star, now 44, six Daytime Emmy Awards as best talk-show host.
In 2002, O'Donnell called it quits to help raise four children with her partner, Kelli Carpenter O'Donnell, as well as launch Rosie magazine. The now-defunct publication quickly fell victim to warring factions and then matching multi-million-dollar lawsuits between O'Donnell and the magazine's parent company, Ultimately, neither side was the victor.
Rosie and Kelli recently appeared together front and center on the HBO special All Aboard! Rosie's Family Cruise, a documentary about the maiden voyage of R Family Vacations, the travel company founded by the two of them and which specializes in gay family vacations.
The View, which debuted in 1997, currently stars Walters, Joy Behar, Star Jones Reynolds and the newest addition, Elisabeth Hasselbeck.
Set to leave The View at the end of next month, Vieira will take Katie Couric's chair opposite Matt Lauer on NBC's Today show this fall, when Couric heads over to the CBS Evening News, where she'll be the show's first solo female anchor.