His mother was a dancer in Broadway musicals who moved to Europe after marrying his father; they fled from the Nazis in World War II and returned to the United States. His father was also musical, playing cello in a symphony outside Chicago in his spare time (while working as a scientist), and his sister is a classical pianist. Graae's first agent urged him to change his surname to "Grey" but he refused, wanting to honour his Danish father. He described Victor Borge, who came to America on the same boat as his father as both fled the 1940 invasion of Denmark, as his main inspiration. In 2007, his mother moved from Tulsa to Los Angeles to live with Graae and his partner. In an interview he said that "life has indeed upheaved as I know it... We're thinking of starting a new sitcom called 'Two Gays, a Dog and an Old Lady.'" Graae came out to his mother in 1983, an experience recalled in his two-hander production "The Prince and the Showboy" with Faith Prince.