Claudia was born in Kuala Lumpur, Malaysia on July 5, 1966. She grew up in Venezuela and then San Francisco, California and after high school, studied voice and dance before pursuing acting as a career. She studied at the American Conservatory Theater and has performed soprano roles with the San Francisco Opera.
Though Wells is most known for her role in Back to the Future, she played many other roles. Most notably, she starred in the series Fast Times, a spin-off of the hit teen movie Fast Times at Ridgemont High. After becoming unable to reprise her role as Jennifer to take care of her mother, who had been diagnosed with cancer, she faded from the acting scene. Wells did however, briefly return by way of voice acting, in which she reprised her role as Jennifer in the 2011 game.
Today, Claudia operates a fashion boutique in Studio City, California called Armani Wells. The store specializes in high-quality men's fashion at low prices. Wells, a single parent, has one child, a teenaged son named Sebastian, and they reside there in Studio City.