But after only one year, Fawcett walked away from the show at the height of her fame to explore a career in film -- a move, the star told Walters, she did not regret.
"I would do it over again ... I felt that I needed to grow," Fawcett said in 1980. "I find that, for me, personally -- and this is in everyday life -- if I'm not growing, if I can't be stimulated in a conversation, then I am bored. And I'm not good when I'm bored."
Jaclyn Smith, one of Fawcett's "Angels" co-stars, told Walters, "I was sad because it was not an actress leaving, it was my friend," but says her friend didn't make a mistake. "When Farrah makes up her mind to do something, uh, it's well thought out, it's well ordered and planned, and it's right for her."
Her career faltered, but Fawcett was determined to take charge of her life. Firing her manager, her publicist and separating from Majors, the sweet blond from Texas revealed to Walters that she was no more.
"I think that when you're kind of just shoved out there and you have to be tough and you're facing tough people and people are saying bad things about you, that all of a sudden, you have to become a little less sweet. ... And with this surge in strength, you lose a little of the softness, I guess," she said.
Tired of being the sex symbol, Fawcett wanted to be taken seriously, so she dove into an unrecognizable role, playing an abused wife, Francine Hughes, driven to kill her husband in the 1984 movie "The Burning Bed."
"I knew that if I wanted to stay in the business, I had to change. I mean, I wanted to change," she told Walters in a later interview.
The TV movie became one of the most highly-rated in history and earned the actress the first of three Emmy nominations.
But if her acting career was finally the triumph she always knew it could be, her personal life wasn't.
After she and Majors parted ways in 1979, Fawcett became romantically involved with actor Ryan O'Neal, who rose to stardom in the 1970 film "Love Story," ironically playing the husband of a woman dying of cancer.
Fawcett and O'Neal carried on a turbulent relationship that spanned two decades. Their first major milestone was the celebrated birth of their son Redmond in 1985.
Though the two never married, they remained one of Hollywood's great love stories.
"I used to ask her to marry me all the time," O'Neal told Walters in an exclusive interview. "But ... it just got to be a joke, you know. We just joked about it."
After 17 years together, Fawcett and O'Neal broke up in 1997.
Four years later, after O'Neal was diagnosed with leukemia, the couple reunited.
"She came right to my side, which I loved her for. And we gradually started to rebuild our relationship," he told Walters.
As Fawcett helped O'Neal to heal, in 2006, she was struck by the devastating death of her mother and diagnosed with anal cancer -- a relatively rare disease that only affects about 5,000 Americans a year.
"I panicked. I didn't let her know, but I panicked," O'Neal told Walters. "I've been living with cancer for eight years at this point and ... I saw lots of what cancer can do. And I just knew one thing, that Farrah Fawcett was hard to kill."