The Latin star first took on the female lead in the play, which features music by Fred Ebb and John Kander, when the production debuted in Chicago, Illinois in 2001.
She led the cast in a performance of The Visit at the Williamstown Theatre Festival in Massachusetts last summer (14) and now it has been booked for a Broadway run at the Lyceum Theatre, with Cheers star Roger Rees also returning to portray Rivera's love interest.
Rivera says, "I'm excited because it has been such a long time but also because we love this piece and really think the American theatre could enjoy a wonderful, interesting, smart musical like this."
The Visit is based on the satirical 1956 Friedrich Durrenmatt play, about a billionaire who returns to her poverty-stricken birthplace in Europe.
John Doyle will direct. Previews will begin in March (15), ahead of opening night on 23 April (15).