The actress was best known for playing Alexis Colby's scheming sister Cassandra "Caress" Morrell in the US soap in the mid 1980s, along with roles in British series Doctor Who, Howards' Way and Triangle.
Her agent Phil Belfield said she died this morning in a Sussex nursing home after a short illness.
He said: "She was extraordinary, she had so much energy and vitality with a love for theatre and acting."
He added: "A shining star has gone out and Kate will be dearly missed by all who knew and have worked with her."
O'Mara's first television roles were in the 1960s. But it was in the 1980s that she landed her biggest and longest-running roles.
As well as Dynasty she starred as a ruthless businesswoman in BBC drama Howards' Way, which was dubbed the "Dallas of the Seas".
She also appeared in the original run of Doctor Who opposite both Colin Baker and Sylvester McCoy as renegade Time Lord The Rani.
Last year, which was Doctor Who's 50th anniversary, she said she would like to reprise the role.
She told the Huffington Post: "I'd love to come back as The Rani another time around.
"To have a much older woman as your adversary, there's something interesting about that."
In the 1990s she starred in the comedy show Absolutely Fabulous as Jackie, the sister of Joanna Lumley's character Patsy.
More recently she had appeared in ITV soap Benidorm and a 2012 stage adaptation of Agatha Christie's Death On The Nile.
She is survived by her sister, the actress Belinda Carroll.
Mr Belfield said there would be a private funeral and a memorial service on a date to be confirmed.
Joan Collins, who played Alexis Colby in Dynasty, paid tribute to O'Mara on Twitter this afternoon.
She wrote: "Tragic news about Kate O'Mara, we had great fun on Dynasty when she played my sister Caress who Alexis insisted on calling CASSIE ! RIP."