Redford has a long association with documentaries
The fund will be used to support up to 50 projects per year and the initial investment will be spread over four years.
"That allows us to kind of put teeth in a commitment that's been long-standing about trying to promote documentaries," Redford said.
Documentary has been a key element of the US film festival in Utah since it was launched 20 years ago by the actor.
Under the plan the money will be used to establish the Sundance International Documentary Fund.
The Sundance cable channel, founded by Redford in 1996 to show independent films, will launch a sister network devoted to documentaries later this year as part of the deal.
Meanwhile, The Man from Elysian Fields, starring Mick Jagger, became the first movie shown at Sundance to find a distributor.
Jagger plays a pimp in the film who runs a circle of gigolos.
Unpredictable
"He's been trying to have a movie career for years, and this is going to give him that career," said Samuel Goldwyn, Jr, who heads the company that bears his name.
The film, shown only to critics so far, will be screened to audiences at the festival on Monday.
Goldwyn added "you can never predict" exactly how audiences will react to films.
Jagger's acting career has so far received mixed reviews.
While he has appeared in 37 films, most have been as himself, and only his role in the 1970 Performance has been given any prise.
His role in the 1992 science fiction film Freejack had a mixed reaction.
More recently, Jagger has turned producer, working on the British thriller Enigma.