The couple met in London while performing in the Andrew Lloyd Webber musical, Love Never Dies.
Boggess -- who will play the lead role of "I" in Rebecca -- received Drama Desk and Drama League nominations for her starring role as Ariel in the Broadway production of The Little Mermaid. She received an Olivier Award nomination for originating the role of Christine Daae in Love Never Dies, and also played that part in The Phantom of the Opera.
Mutu -- who will play Maxim de Winter, the new husband of "I" in Rebecca, has previously appeared in such shows as Chess, Loves Labours Lost, Anything Goes, South Pacific, and Royal Hunt of the Sun.
Rebecca will begin previews at the Broadhurst Theatre on March 27, in anticipation of an April 22 opening.