The British actress was best known for her role as sister to Joan Collins' Alexis Colby in the US soap.
She also had prominent roles in the '80s series Howards' Way and Triangle, and in Doctor Who.
Her agent said she died in a Sussex nursing home following a short illness.
He praised her "energy and vitality" and her "love for theatre and acting".
"A shining star has gone out and Kate will be dearly missed by all who knew and have worked with her," said agent Phil Belfield, who labelled the actress "extraordinary".
O'Mara's first television roles were in the 1960s, but she came to public attention playing the manipulative Cassandra "Caress" Morrell in Dynasty.
Co-star Joan Collins tweeted: "Tragic news about Kate O'Mara , we had great fun on Dynasty when she played my sister Caress... RIP."
O'Mara played a ruthless businesswoman in BBC drama Howards' Way and was briefly a regular on the North Sea ferry drama Triangle.
She also appeared in Doctor Who, opposite both Colin Baker and Sylvester McCoy, as renegade Time Lord The Rani - a role she said she would love to return to.
"If you put a much older woman in Doctor Who, they can identify with it," she told Digital Spy ahead of the 50th anniversary celebrations for the show, where she tweeted images of herself with former co-stars.
"I think it's quite an interesting concept and if you remember things like Grimm's Fairytales, the older woman is often the villainess, often the terrifying figure - why I do not know, but often she is. I think it's an idea to be exploited."
On hearing the news of her death, Doctor Who co-star Baker tweeted: "Oh my goodness. Kate O'Mara is no longer with us. Sad sad news. A delightful, committed and talented lady and actress. We are the poorer."
In the 1990s, O'Mara starred in BBC comedy Absolutely Fabulous as Joanna Lumley's on-screen sister Jackie, and in 2001, she made a string of appearances in ITV drama Bad Girls.
More recently she had appeared in ITV soap Benidorm and a 2012 stage adaptation of Agatha Christie's Death On The Nile.
One of her final public appearances saw her hosting An Evening With Kate O'Mara in London last October.
She published two autobiographies and two novels, When She Was Bad and Good Time Girl.
She was married to actors Richard Willis and Jeremy Young and leaves a sister, actress Belinda Carroll. Her son Dickon died last year.
The actress last posted a message on Twitter on 17 March.
"Thank you so much for your kind tweets," she wrote.
"It's both humbling and completely overwhelming to read all of your messages. Much Love x."