The actor was born in 1927 in Recklinghausen and raised in Hamburg. Already in 1947 he was with the Hamburg Chamber of playing on stage, he later starred in over 80 feature films. He was, among other things for the remake of the Heinz Rühmann films "Three from the gas station" (1955) and "The Feuerzangenbowle" (1970) in front of the camera in "Charley's Aunt" (1956) and "The Captain from Koepenick "(1956) he played together with Rühmann. He also starred in the television series "The Love Boat" with.
For his role as a former Army private first class in "Roses for the Prosecutor" Giller was awarded the 1960 National Film Award, in 2000 he was honored with his wife, Nadja Tiller [1929- ], with the Federal Cross of Merit.
Giller and Tiller were already in the 1950s and 1960s a dream couple among German actors. The two actors were married in 1956 and had two children together. Since 2008, Giller and Tiller lived in a Hamburg retirement home. Giller appeared in three Euro-westerns: "The Last Ride to Santa Cruz", "The Legend of a Gunfighter" (both 1964) and "Legacy of the Incas" (1965).