Dancing Queens all over the world will no doubt rejoice.

“Mamma Mia!” — the tuner that made theater snobs cringe but that worldwide auds embraced — has fueled the bigscreen interest of Playtone partners Tom Hanks and Gary Goetzman.

They closed a deal with Littlestar — the company run by the show’s producer, Judy Craymer — and Abba songwriters Benny Andersson and Bjorn Ulvaeus, and they are in talks with Universal to finance and distribute.

The filmmakers are eyeing release by late 2007. The show’s book writer, Catherine Johnson, is penning the screenplay, which will stick closely to the crowd-pleasing musical’s plot. Raised on a Greek island by a formerly rebellious mom who never disclosed the identity of her father, a bride-to-be locates three men who might be her father and invites them to her wedding. The resulting conflict triggers 22 Abba hits like “Dancing Queen,” “Take a Chance on Me” and “The Winner Takes It All.”

Craymer, who has opened the jukebox musical in 130 cities around the globe, will produce with Goetzman. Hanks, Rita Wilson, Andersson and Ulvaeus exec produce.

Craymer had rebuffed film offers for years but liked the Playtone pitch and what Hanks, Goetzman and Wilson had done to turn Nia Vardalos’ one-woman stage show into “My Big Fat Greek Wedding.” Craymer will be as closely involved in the film as she is in the 11 productions of the show currently playing worldwide.

Craymer and Johnson were broke when they first tried to put the show together and were even snubbed by the Swedish pop group whose music formed the basis for the show. They are now two of the wealthiest women in England.

Craymer’s marriage of plot and Abba tunes is a global juggernaut that has grossed $1.6 billion since its London opening in 1999. It has been steadily among Broadway’s top five grossing shows since opening five years ago and averages over $1 million a week in ticket sales.

“The time felt right. The partnership with Gary and Tom helped everything to fall into place,” Craymer said. “We’ve never had stars in the show, the music has always been the star, but we are certainly thinking about names as we take this from the stage to the screen.”