The show is to open at The Civic in Auckland in April.
"'Jersey Boys' is world-class and the biggest musical to visit Auckland for some time," Brown said in a statement. "It will attract many visitors to the city, showcasing Auckland as an entertainment destination."
"Jersey Boys" opened in Melbourne in July 2009 and played for 13 months before transferring to Sydney's Theatre Royal, opening in September 2010.
More than 1 million people will have seen the show in Melbourne and Sydney by the end of the year. It then will go directly to Auckland.
Broadway producer Michael David of Dodger Theatricals said: "We are thrilled to bring 'Jersey Boys' to New Zealand. This story of Frankie Valli and The Four Seasons has captivated nearly 13 million fans in productions worldwide, and now it is our fondest hope that New Zealand will embrace 'Jersey Boys' in the same way. The show is chock-full of classic Four Seasons show-stopping songs and a story that is all the more riveting because it's true."