One of the most successful musicals in history is set to come to Adelaide, bringing its reputation for controversy and booming box office sales to the city of churches.

It will also show in Brisbane.

Advertisements for The Book of Mormon have started popping up at bus stops across the two cities, proclaiming "the Mormons are coming!".

Social media accounts for the Book of Mormon have also hinted that "Good things come to those who waitlist" along with a picture of a bus stop ad in Brisbane.

The ABC understands the musical hit will be landing in Adelaide next year.

It is not known when it will open in Brisbane.

The musical tells the story of two young Mormon missionaries who travel to Uganda to preach the religion.

Posters for the musical have started appearing around Adelaide. (ABC News: Alina Eacott)

It was written by South Park creators Trey Parker and Matt Stone and was first performed on Broadway in 2011.

It has played in front of capacity crowds in New York every week since then, and has also sold out every single performance in London's West End since opening in 2013.

The musical has been staged around the world, and won nine Tony Awards when it opened.

It was named best musical at last year's Helpmann Awards for Australian theatre.

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That accolade came during a year-long season in Melbourne which ended in February.

It is now enjoying the same success in Sydney, where it set a sales record.

Promoters said "more than 45,000 tickets [were] sold by the end of the first day of public sales … with a value of over $5,000,000".

The satirical musical has been controversial, although the Mormon Church has been creative in its response.

On Broadway, the church took out advertisements in a popular theatre booklet accompanying the show.

In Melbourne, The Church of Jesus Christ of Latter-Day Saints ran advertising in some of the city's busiest locations and prime-time TV advertising, with slogans like "you've seen the show, now read the book".

An official announcement of the show's Adelaide season is expected soon.

SA Tourism Minister David Ridgway said it would be "fabulous" for the city to host such a successful production.

"We're a great city to bring events to, it's a great city to visit," he said.