Greene was born in Las Vegas, Nevada, to an Irish-American father, Roland, and a Mexican/Nicaraguan mother, Dorita, who was an accomplished singer and dancer.

She attended the University of Southern California,[4] where she auditioned for and was accepted to the Bachelor of Fine Arts program, entering on a scholarship and beginning her formal training as an actor.

Shortly after graduation, she landed the role of Judy Nuckles in the short-lived Steven Bochco series Bay City Blues (1983).

[4] The show was a critical and commercial success, winning multiple Emmys and garnering Greene a nomination in the Best Supporting Actress category in 1989.

[6][7] After leaving L.A. Law, Greene had acting roles in a number of popular television series including Bones, CSI, CSI: Miami, Cold Case, Crossing Jordan, Diagnosis: Murder, JAG, Judging Amy, Nip/Tuck, The Outer Limits, Six Feet Under, Stargate SG-1 and The Unit.