Her maternal grandfather, Mikhail Baronov, was a senior officer in the Russian Navy; his wife, the former Lydia Vishniakova, was a general's daughter. Tennant has a sister, Irina, and a brother, Robert, both of whom were seriously injured in a car accident in 1967, in which their father was killed. Tennant's godfather was the actor Laurence Olivier.
Tennant's first marriage was to Peppo Vanini, a nightclub owner who owned the famous Xenon nightclub, in 1969 (divorced, 1976). She dated Matthew Chapman, a Writer and Director from in 1978 until 1982, but ended their relationship upon meeting actor–comedian Steve Martin. She married Martin in 1986, and they divorced in 1994. Since 1996, Tennant has been married to Kirk Justin Stambler, a Lawyer for Warner Bros., with whom she has a daughter, Katya Irina, and a son, Nikolai.
In 2014, she published a memoir about her mother titled Irina Baronova and The Ballets Russes de Monte Carlo, published by the University of Chicago Press. The book was presented at the Bel Air Country Club in Bel Air, Los Angeles.
