Scorsese, who scooped a long overdue best director Oscar at February's Academy Awards, will begin production on the project later this year but the film is expected to take several years to complete, Daily Variety reported.
"It would have given George great joy to know that Martin Scorsese has agreed to tell his story," Variety quoted Harrison's widow, Olivia, as saying.
Olivia Harrison is to serve as a producer on the film, which will include participation from the two surviving Beatles, Paul McCartney and Ringo Starr.
It is the latest in a series of music based documentaries that Scorsese has directed, following the 2005 Bob Dylan film "No Direction Home" and the upcoming "Shine A Light" about The Rolling Stones.
The Harrison film will focus on his time in the Beatles as well as his solo career and interest in Eastern mysticism, Variety reported.
"George Harrison's music and his search for spiritual meaning is a story that still resonates today and I'm looking forward to delving deeper," Scorsese told the paper.

Copyright AFP (Agence France-Presse), 2007