His film will focus on the period from their days performing in Liverpool's Cavern Club and their Hamburg residency up to their final paying concert in San Francisco's Candlestick Park in 1966.
The story was previously covered extensively in the Beatles Anthology series of films in the 1990s.
Howard - who picked up an Academy Award for A Beautiful Mind - will cover what are known as "the touring years" in his film. After the Candlestick Park show, the Fab Four concentrated on the studio, playing publicly on only one other occasion with their rooftop gig in 1969 at their Savile Row HQ in London.
The new film is being made with the "full cooperation" of Sir Paul McCartney and Ringo Starr, as well as the widows of John Lennon and George Harrison - Yoko Ono and Olivia Harrison.
Howard said he was "excited and honoured" to be working "on this astounding story of these four young men who stormed the world in 1964".
He added: "Their impact on popular culture and the human experience cannot be exaggerated."
It was the band's visit to the US in early 1964, along with a first celebrated appearance on popular US programme The Ed Sullivan show, which demonstrated the impact they had made on a global scale.