The 34-year-old British model has filed legal papers at the LA County Superior Court.
Mr Sanders, 41, was photographed last year in an intimate moment with the American actress, 22, whom he had directed in the film Snow White and the Huntsman.
In the film Miss Stewart, 22, played Snow White while Miss Ross was cast as her mother.
One of Miss Ross’s friends described the encounter between Mr Sanders and Miss Stewart as “one of those silly flirtations”.
“She is prepared to give Rupert a second chance,” the friend said last year.
The director’s father, Michael Sanders, a retired surgeon, said at the time of Miss Stewart: “This girl’s a pretty young thing and if you’ve been gadding around for five months, or what have you, you’re bound to get a bit friendly. This kind of thing gets blown out of all proportion.”
Miss Ross, who is being represented by Laura Wasser, a high-profile divorce lawyer, is said to be asking for joint custody of the couple’s two children, as well as financial support from Mr Sanders.
Mr Sanders has filed a response to the divorce, also asking for joint custody of the couple’s children, Skyla, seven, and Tennyson, five.
Miss Stewart issued a statement after photographs of her “flirtation” with Mr Sanders appeared last year.
"I’m deeply sorry for the hurt and embarrassment I’ve caused to those close to me and everyone this has affected," she said.
"This momentary indiscretion has jeopardised the most important thing in my life, the person I love and respect the most, Rob. I love him, I love him, I’m so sorry."
Meanwhile Miss Ross is said to have formed a friendship with Jimmy Iovine, the American music producer.
The pair were seen together at parties after the Golden Globe Awards in Los Angeles earlier this month.
“There’s no indication anything has happened, but there is a lot of attraction between them,” a source said.