Russo was born in Burbank, California, the daughter of Shirley (née Balocca), a factory worker and barmaid, and Nino Russo, a sculptor and car mechanic who left the family when Rene was two.Her father and maternal grandfather were of Italian descent. Russo grew up with her sister, Toni, and their single mother. She attended Burroughs High School (where her classmates included director Ron Howard), but eventually dropped out in the tenth grade. To help her family, she began taking a variety of part-time jobs including working in an eyeglass factory, and as a movie cashier.
By her 30th birthday, demand for her as a model began to dwindle. She did a few more commercials and then turned her back on modeling and show business for a while. She began to study theater and acting, and began appearing in theater roles at small regional theaters in Los Angeles and elsewhere in California.
Russo made her television series debut in 1987, with a supporting role in the TV series Sable. Two years later, she made her debut in film as the girlfriend of the Tom Berenger character in Major League. Her breakthrough role is generally considered to be her part as internal affairs detective Lorna Cole in Lethal Weapon 3 (and again in Lethal Weapon 4) opposite Mel Gibson.
Throughout the 1990s, Russo appeared in a number of thrillers including In the Line of Fire with Clint Eastwood, Outbreak with Dustin Hoffman, Ransom (directed by high school classmate Howard) and The Thomas Crown Affair. She attained a certain degree of cult status from her performance in Freejack, alongside of Emilio Estevez, Mick Jagger, and Sir Anthony Hopkins.
She also tried her hand at comedy in Tin Cup with Kevin Costner, Get Shorty with John Travolta and as Natasha Fatale in the live-action film version of The Adventures of Rocky and Bullwinkle. She starred in at least one major studio film per year from 1992 to 2002.

In 2005 Russo co-starred with Al Pacino in Two for the Money and with Dennis Quaid in Yours, Mine and Ours. In 2011, six years after resting from acting, she appeared in the superhero film, Thor, as Frigga, the mother of the titular hero.