It was actually the idea of media mogul David Geffen to put the production on stage, approaching Brooks but thinking someone else would compose new music for it.
But the backers turned to Brooks to create new tunes for the stage production.
There were of course reservations about whether a musical film about a musical would work as a real stage musical.
Musical star Leigh Zimmerman is part of the West End cast
But when the production first opened on Broadway, with Nathan Lane and Matthew Broderick in the lead roles, it was instantly declared a hit by reviewers and quickly began to sell out.
Although keeping the essence of the film, and the centre piece song Springtime for Hitler, Brooks updated it with new songs and gave some characters more prominent roles, including that of secretary Ulla.
Its overwhelming success was compounded by winning the most Tony Awards in history, picking up a total of 12 in 2001, including best musical and director.
But the production hit problems when Lane and Broderick bowed out.
British actor Henry Goodman was fired from his role as Max Bialystock after just 30 performances, with no notice.
The producers of the show said Goodman was right to feel angry at this treatment and that he was a fine actor but just not right for the part.
Eventually Broderick and Lane returned to their roles for a 14-week run in 2003, much to the delight of fans.
It success on Broadway meant there were calls for it to transfer to London as soon as possible.
The lead actors for the West End were announced as Lee Evans and Richard Dreyfuss.
It was considered something of a coup to secure Oscar winner Dreyfuss despite the fact his musical credentials were largely unknown.
And the demands of musical theatre took its toll on the 56-year-old who parted company with the show just days before the curtain was supposed to rise in the West End for preview performances.
Luckily for the real producers, and the those who had already booked tickets, Nathan Lane was available to step back in the role.
It gave him the chance to team up once again with Lee Evans, with whom he had appeared in film The Mousehunt, and secure a bumper pay packet.
If he had not stepped into the breach, there was a real risk the show would not go on.
But the knock-on effect of Lane heading to London is the delay to filming a remake of The Producers - in which he will star with Broderick.
The film will be directed by Susan Stroman, who has made such a success of it on Broadway.
Nicole Kidman is slated to appear in the film as Ulla.
The remake continues the Hollywood revival for musical films such as Chicago and Moulin Rouge.
And it could bring The Producers to a new generation who perhaps will not pay the high West End or Broadway prices to see the musical.
[source: BBC News Online]