After working initially as a short story writer, Kosterlitz was hired by a Berlin movie company as scenarist, becoming an assistant to director Curtis Bernhardt.

Koster was in the midst of directing his second film Das häßliche Mädchen, when Hitler and the Nazi party rose to power.

He automatically lost his German citizenship (as did all German Jews) in 1933, when Hitler became chancellor, and managed to complete his second film before being forbidden to make films under the intense, legalized antisemitism, (i.e. persecution of Jews) which accompanied Garmany's embrace of Hitler and Nazism.

One of those films was Catherine the Last after a script by Joachimson and Károly Nóti that was remade in 1938 by Norman Taurog as The Girl Downstairs, both versions starring Franciska Gaal.

Although Koster did not speak English, he convinced the studio to let him make Three Smart Girls, for which he personally coached 14-year-old star Deanna Durbin.

Koster's second Universal film, One Hundred Men and a Girl, with Durbin and Leopold Stokowski also was successful.

He directed more costume dramas, including Désirée (1954) with Marlon Brando, The Virgin Queen (1955) with Bette Davis, The Naked Maja (1958) with Ava Gardner and The Story of Ruth (1960) with Elana Eden, then returned to family comedies and musicals, including Flower Drum Song for Universal in 1961.

Koster retired to Leisure Village in Camarillo, California, where he painted a series of portraits of the movie stars with whom he worked.

Although Koster never won an Oscar, he directed six different actors in Oscar-nominated performances: Cecil Kellaway, Loretta Young, Celeste Holm, Elsa Lanchester, Josephine Hull, James Stewart and Richard Burton.

The archive has preserved a number of these home movies, including behind-the-scenes footage from some of Koster's films.