The opera singer worked as a mobile phone salesman at Carphone Warehouse until he won the ITV1 reality series last year.
The show's creator Simon Cowell will produce the film with Relevant Entertainment's Michael Menchel and Steve Whitney for Paramount Pictures.
Menchel called him to suggest a movie after seeing Potts's performances on YouTube, and Paramount executives were similarly impressed, reports Variety.
Talking about the tenor's first audition, Cowell said: "That particular day was one of the worst, the acts were just terrible, we were fed up and on comes this guy with a funny little suit and bad teeth who looked very nervous.
"I can remember looking at the other judges, with that 'here we go again' feeling. We had 2,000 people in the audience, and I'll never forget how much the room changed when he began singing."
He added that he felt a big-screen version of the story would appeal to movie-goers, saying: "Most of these calls result in absolutely nothing, but this company got that it's another Billy Elliot, a story anyone in the world can understand.
"This was his last chance, and he literally decided to enter based on the toss of a coin. And despite his success off the back of the show, the only difference I see in him is that he got his teeth fixed."
Potts' debut album One Chance topped the UK chart last July and has sold 3 million copies.
> Paul speaks to DS about his Britain's Got Talent win