Sheridan was born in Worthing, England, the daughter of actress Sally Adams, who gave birth to her at age 16. When Sheridan was less than a year old, her father left the family, and she has not seen him since.
In 1969, her mother Sally (billed as Dani Sheridan) featured in the James Bond film On Her Majesty's Secret Service as one of Blofeld's "Angels of Death". There, Sally met Blofeld actor Telly Savalas, who eventually became her de facto husband and Sheridan's stepfather. Sally became known as Sally Savalas.
Sheridan emigrated to the United States from the United Kingdom in 1973, when she was 10 years old.