The film beat strong competition from "Black Panther," "BlacKkKlansman," "Bohemian Rhapsody," "The Favorite," "Roma," "A Star Is Born" and "Vice."
Directed by Farrelly and set in the 1960s, "Green Book" follows African-American classical and jazz pianist Don Shirley and Tony Vallelonga, an Italian-American bouncer who serves as Shirley's driver and bodyguard, on a tour through the racially divided South.
The film also won another two Oscars awards on February 24 for Best Supporting Actor and Best Original Screenplay.
Mahershala Ali, who played the jazz pianist in the movie, was named Best Supporting Actor.