The death follows the passing of several 007 stars over the past year – including Honor Blackman, Diana Rigg, and Sean Connery.
The star had been in hospital after collapsing at her home in Los Angeles on Christmas Eve, her agent said and died on Sunday.
Her cause of death has not been released, but it was confirmed that it was not due to COVID-19.
Lance O’Brien, her partner of 18 years, was able to be with her in the moments before.
Roberts was known for playing Stacey Sutton, the granddaughter of a California oil tycoon, opposite Roger Moore’s 007 in the 1985 movie A View To A Kill.
She also played Midge Pinciotti in That ’70s Show, alongside Mila Kunis and Ashton Kutcher, from 1998 to 2004, and became a Charlie’s Angel in 1980 with Jaclyn Smith and Cheryl Ladd, playing Julie Rogers in the final season of the hit show.
Mike Pingel, her publicist, and friend of more than 20 years told Sky News the actress was a big animal lover who “lived for her animal babies”, which included her two dogs, Muttley and Socks, a bird and Koi fish.
Paying tribute, he said: “I’m devastated, I’ve been friends with Tanya for over 20 years.
“She was full of boundless energy and we always had the best times. She was truly an angel and I will miss her so so much.”
Mr. Pingel added: “One of my favorite memories with Tanya was driving in the car and Duran Duran’s A View To A Kill theme song came on the radio – we both sang along. Priceless.”
In a joint statement, James Bond producers Michael G Wilson and Barbara Broccoli paid tribute, saying: “We are saddened to hear of the passing of Tanya.
“She was a very lovely person and shall always be remembered by Bond fans as Stacey Sutton in A View To A Kill. Our heart goes out to her family and friends.”
Roberts’ other screen credits included the titular role in Sheena, a female version of the Tarzan story, in 1984, and the adventure film The Beastmaster in 1982.