Russo, an Italian American, was born in Burbank, California to Shirley Balocca (a workwoman and barmaid) and Nino Russo, a sculptor and mechanic who left the family when Rene was 2. 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. Due to financial constraints within the family, she began taking a variety of part-time jobs, working as a restaurant hostess, a Disneyland cashier, a movie theatre concession stand worker, and as a contact lens inspector at an eyeglass factory.

In 1972, Russo was spotted at a Rolling Stones concert by a scout and manager from International Creative Management. She was signed to the Ford modeling agency and began modeling shortly after, appearing on several magazine covers, including that of Vogue. Russo spent the majority of the 1970s and early 1980s modeling, but later began to study acting, and appeared in roles at regional theaters in Los Angeles.

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 lead character in Major League. Her first major breakthrough role is generally considered to be her part as an internal affairs detective in Lethal Weapon 3 (1992).

Throughout the 1990s, Russo appeared in a number of high-profile thrillers that were successful at the box office, including In the Line of Fire, Outbreak and Ransom. She has starred in at least one major studio film per year from 1992 to 2002.

Although she did not appear in any films in 2003 or 2004, she starred in both Two for the Money and Yours, Mine and Ours in 2005.