The film, the first to be produced and financed by fledgling Los Angeles-based L+E Productions, will receive its world premiere on January 21.
Fleming and Pam Brady co-wrote the story, which stars Coogan as a high school drama teacher who creates a musical sequel to Shakespeare. CAA is handling sales.
L + E principals Eric Eisner and Leonid Rozhetskin produced with Aaron Ryder. Bona Fide Production's Albert Berger and Ron Yerxa, who produced Little Miss Sunshine, served as executive producers.
'It is not unusual for us to add films to our lineup - especially very funny films which we know will have immense appeal,' festival director Geoffrey Gilmore said.
'Hamlet 2 fits the bill perfectly. In addition to being a clever comedy, the film features a number of actors who are part of the extended Sundance family. It's fitting to have them here.'
Rozhetskin, who worked extensively in the NHL, founded L+E Productions with Eisner two years ago with the aim of making films across all genres and providing equity funding for projects in the $5-25m range.