Interviews and early production will begin this year, and the film will take several years to complete, the trade paper said.
"It would have given George great joy to know that Martin Scorsese has agreed to tell his story," the paper quoted Harrison's widow, Olivia, as saying.
She will serve as a producer of the untitled project, and will supply archival materials. Daily Variety added that surviving Beatle members Paul McCartney and Ringo Starr would participate, as would the Beatles' Apple Records label.
Scorsese, who won an Oscar this year for directing the crime saga "The Departed," is preparing for the April 2008 release of a concert documentary about the Rolling Stones, called "Shine A Light." He turned his attention to Bob Dylan in the 2005 documentary "No Direction Home," and depicted the Band's farewell concert in 1976's "The Last Waltz."
The Harrison movie will cover his time in the Fab Four, when he composed such memorable tunes as "Something" and "Here Comes the Sun," his inconsistent solo career, his foray into movie production with such projects as "Monty Python's Life of Brian," and his enthusiastic embrace of Eastern mysticism, Daily Variety said.www.reuters.com