Stronach was born to Israeli and Scottish parents. Her father, David Stronach, is a renowned archeologist of ruins of Ancient Persia (modern-day Iran) and a professor at UC Berkeley. David met his wife, an Israeli archeologist named Ruth Vaadia, in Tehran, where they both worked on excavations at a Tehran site. They got married shortly afterwards, and Tami is their second child.
The family fled to Israel during the Iranian Revolution in 1978 where they lived for a few years until the family had to relocate again to America for a job David got as a professor of archeology.
Stronach made her acting debut as "The Childlike Empress" in The Neverending Story (1984), a film adaptation of the novel Die Unendliche Geschichte (The Neverending Story) by Michael Ende. She has not since had many known acting roles; her parents preferred that she not further pursue acting to avoid the possible dangers many child actors in both movies and television sometimes encounter. She has nevertheless since acted in Chambre at La Ma Ma, and she has further studied acting with Laura Esterman. More recently, she has suggested that she would like to return to acting after her hiatus.
She also released a 45 rpm single around the same time as The Neverending Story entitled Tami Stronach - Fairy Queen. The songs on the album are called "Fairy Queen" and "Riding On a Rainbow." The tracks are of similar synthpop orientation as the Giorgio Moroder/Limahl Neverending Story theme, and may have been an attempt to capitalize on its success.
Since the days of her childhood role, she has become a member of a well-respected Israeli dance troupe based in the U.S, the Neta Dance Company, joining them in 1996, she performed with the company mostly in places like the U.S, Israel and Europe. She has also choreographed and performed her own works, including "The Maid and the Marmalade" and "Contain yourself, darling." While her own work has typically been performed in New York City, she has begun more recently to take this abroad, such as with a tour of Australia in July 2006.
She is married to Greg Steinbruner since April 30, 2010. They had a daughter (born in January 2011).