Dozier was married to Katherine Foley from 1929 until their marriage ended in divorce in 1946. They had one son, Robert. Then, Dozier married Joan Fontaine from 1946 until they divorced in 1951. They had one daughter, Deborah. Lastly, Dozier married Ann Rutherford in 1953. Their marriage would last until Dozier died in 1991.
He began in the film industry. With Joan Fontaine he co-founded Rampart Productions, responsible for Letter from an Unknown Woman (1948). In the early 1950's he was Executive Producer for dramatic programs on CBS television including You Are There, Ben Hecht's Tales of the City and Suspense.
He is best remembered as the executive Producer and narrator of the Batman television series (1966–1968), although he was uncredited for the role as narrator. He also performed those functions on The Green Hornet television show, which starred Van Williams and Bruce Lee, although here the narration was limited to the opening, the next-episode trailers, and the story-so-far recaps in its three two-part episodes. Dozier also made a screen test of an aborted version of Wonder Woman in 1967. During his time as executive Producer of Batman he co-created the character Barbara Gordon, who would become a prominent character in the Batman comic books as well as the TV series.
In 1979, Dozier appeared in The Paper Chase as Lindsey in "Scavenger Hunt," Episode 22 of Season 1.
