Griggs joined the staff of Paramount Pictures in 1924 after graduating from school and initially worked at the studio's process department.

Griggs won the Academy Award for Best Cinematography for the 1953 Western Shane.

[2] Griggs' other Paramount films as cinematographer included the 1954 musical White Christmas, the 1956 Cecil B. DeMille epic The Ten Commandments, and the Jerry Lewis comedies The Sad Sack (1957) and Visit to a Small Planet (1960).

He was also the cinematographer on George Stevens' 1965 United Artists release The Greatest Story Ever Told as well as Otto Preminger's World War II drama of that same year, In Harm's Way.

His final film was the 1971 American International Pictures comedy Bunny O'Hare starring Bette Davis and Ernest Borgnine.