The tapes were made for a book written by Andrew Morton and include passages about her marriage to the Prince of Wales and her suicide attempts.
The film is called The Biographer: The Secret Life of Princess Diana, and tells the story of her collaboration with Mr Morton.
It is due to be screened by the CBS network on 1 September, the fifth anniversary of her death.
'Untold story'
Paul McGann stars as the former Fleet Street journalist who received the tapes from a mysterious intermediary played by Notting Hill actor Hugh Bonneville.
The acting blends with real footage of Diana, and the actual recordings she made for the book Diana: Her True Story.
The film's makers said they decided it would have been impossible for an actress successfully to portray the Princess.
Director Philip Saville was initially sceptical about making the film.
But he said: "After I read the screenplay, I was so much touched and convinced that there is an important and unknown story which must be told about the Princess."
Brian Cox, who plays the publisher Michael O'Mara, said: "The script tells a revealing story of a man who was caught up in something which he was not really in control of because she had chosen him."
The film has taken three years to make and was produced with the full co-operation of Mr Morton.
There are currently no plans to screen it in the UK.