Eva Noblezada, 17, will make her professional stage debut in the production.
She was reportedly first spotted at a school awards show in New York (see video) by Broadway casting director Tara Rubin, who recommended her to Mackintosh.
Briones was in the ensemble in the original cast of Miss Saigon when the show opened at the Theatre Royal, Drury Lane. He has since played the role of The Engineer in his native Philippines and on tour in both the UK and US and also in Germany.
Brammer made his professional stage debut in Les Miserables and subsequently appeared in the Oscar-winning movie adaptation. Carroll was recently seen in Mackintosh's production of Barnum at Chichester, and has previously appeared in the West End as Nancy in Oliver!
Miss Saigon will open in May 2014 and is directed by Laurence Connor, who reconceived the show for its UK and international tour and also recently revamed Les Miserables (with James Powell) for its 25th anniversary tour.
Written by Les Mis composers Alain Boublil and Claude-Michel Schonberg, Miss Saigon transplants the Madam Butterfly story to war-torn Vietnam. Cultures and aspirations clash when a local prostitute meets her GI Joe during the fall of Saigon in 1975.
Directed by Nicholas Hytner and produced by Mackintosh, the original production ran at the Theatre Royal, Drury Lane from 1989 to 1999. It starred the then unknown Lea Salonga as Kim, alongside Jonathan Pryce as the Engineer and Simon Bowman as Chris.