"After reviewing all the footage and audio that Michael Lindsay-Hogg shot 18 months before they broke up, it's simply an amazing historical treasure-trove. Sure, there's moments of drama - but none of the discord this project has long been associated with.
"Watching John, Paul, George, and Ringo work together, creating now-classic songs from scratch, is not only fascinating - it's funny, uplifting and surprisingly intimate.
"I'm thrilled and honoured to have been entrusted with this remarkable footage - making the movie will be a sheer joy."
Jackson has teamed up again with his They Shall Not Grow Old partners, producer Clare Olssen and editor Jabez Olssen. The footage will be restored with techniques developed for the first World War documentary film which has been nominated for a BAFTA for best documentary.
The new film is being made with the cooperation of Paul McCartney, Ringo Starr, Yoko Ono and Olivia Harrison, the widows of John Lennon and George Harrison.
The film was announced on the 50th anniversary of the Beatles' final performance on the roof of Apple Records in London.
According to the Beatles website, the footage was originally planned for a TV special.
In addition to the Jackson-directed film, a restored version of the original Let It Be movie directed by Michael Lindsay-Hogg will also be made available.