When British production company Celador first approached director Danny Boyle with the script for Slumdog in 2006, the veteran director was skeptical. Boyle wasn't thrilled with the idea of making a movie about Who Wants to Be a Millionaire?—much less for the company who originally rose to prominence by producing the actual show. (Source) Before long, however, the strength of the script won out, and Boyle committed to the project.
The following summer, Celador's Christian Colson, with the backing of fellow British studio Film4 (which would go on to work with Boyle again in 2010's 127 Hours) reached out to U.S. distributor Warner Independent Pictures who ponied up for $5 million, enough to begin production. (Source)
Filming began in November 2007, but by May of the following year, Warner Independent had been folded into its parent studio, Warner Bros. Doubting the commercial appeal of Slumdog, Warner Bros. pushed for a straight to DVD release. (Source)
Fortunately for theatergoers in the U.S., Fox Searchlight, Fox's indie movie division (think Juno, Little Miss Sunshine, and Birdman) intervened, tapping the film for theatrical release. Sure enough, it worked out in their favor, becoming Searchlight's highest grossing film of all time… and definitely making millionaires out of the guys who made Millionaire.