The film will feature new interviews with Jimmy Page, Robert Plant and John Paul Jones, as well as previously unseen footage.
Directed by Bernard MacMahon, the documentary is now in post-production and comes after the band celebrated their 50th anniversary milestone last year.
It is set to be introduced to buyers at Cannes Film Festival next week.
Announcing the film, bassist Jones said: "The time was right for us to tell our own story for the first time in our own words, and I think that this film will really bring that story to life."
New interviews with Page, Plant and Jones form part of the film, as well as rare archival interviews with Bonham, who died in 1980.