O'Neal added: "Although this is an extremely difficult time for her family and friends, we take comfort in the beautiful times that we shared with Farrah over the years and the knowledge that her life brought joy to so many people around the world."
Fawcett's spokesman, Paul Bloch, said she had died shortly before 0930 local time on Thursday in a Santa Monica hospital.
O'Neal and Fawcett's friend Alana Stewart - singer Rod Stewart's ex-wife - were by her side, Mr Bloch added.
Stewart said in a statement: "For 30 years, Farrah was much more than a friend, she was my sister, and, although I will miss her terribly, I know in my heart that she will always be there as that angel on the shoulder of everyone who loved her."
The star's former Charlie's Angels co-star Jaclyn Smith said: "Farrah had courage, she had strength, and she had faith."
The actress, who played Kelly Garrett in the hit TV series, added: "And now she has peace as she rests with the real angels."
Cheryl Ladd, who played Kris Munroe in the show, said: "I'm terribly sad about Farrah's passing. She was incredibly brave, and God will be welcoming her with open arms."
John Forsythe, who played a mysterious behind-the-camera boss in Charlie's Angels, said: "She put up a gallant fight against her unforgiving disease, and I send my deepest sympathies and prayers to her family and friends."
The screen star was previously married to Lee Majors, star of The Six Million Dollar Man, from 1973 to 1982.
"She was an angel on Earth and now an angel forever," Majors said.
Oscar-winning actor Robert Duvall, Fawcett's co-star in 1997 film The Apostle, said she was "an outstanding talent - better than most feature film actresses that I've seen".
Her death has come just weeks after her TV documentary was broadcast.
The video diary chronicled her battle with anal cancer in her final months.
O'Neal said she had wanted to tell her story on her own terms.
O'Neal, Fawcett's partner since 1982, recently disclosed they would finally get married, but the pair never got the chance to exchange vows.
She and O'Neal have one son, Redmond, who is serving a prison sentence for drug offences.
As Fawcett's career was taking off, she posed in a red bathing suit for a poster which went on to sell several million copies.
Her long blonde locks, made famous by her role in Charlie's Angels, were emulated by fans across the globe.
The actress earned a string of Emmy and Golden Globe nominations for her small screen roles, but never won one of the major awards.
In 1995, she was honoured with a star on the Hollywood Walk of Fame.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.