Streeter was born to Jim and Sandra Dailey in the Cayman Islands. She has two sisters and a brother. She was educated in England at the independent girls' school Roedean and at Brighton University. She met and married her husband Paul Streeter in England. They moved to the Cayman Islands in 1995. They have a daughter, Tilly Annina Andrus Streeter (b. 19 August 2008) and a son, Charlie Streeter (born 2015). After giving birth Tanya Streeter officially retired from freediving. She currently resides in Austin.