The Sony Award-winning actress died peacefully in her sleep on Monday.
She was best known for her role as Effie Macinnes in the STV soap opera Take The High Road, in which she starred from the early 1980s until the last episode in 2003.
Riggans also played Suzie Sweet in the BBC children's programme Balamory from 2002 to 2005 and appeared in other television shows such as Rab C Nesbitt and Taggart.
Her death was confirmed by Martin Hunt, a friend and spokesman for the family.
"She died peacefully holding her daughter's hand at 4.40pm on December 2 2013," he said.
Riggans had a stroke in April last year, which left her with speech and movement difficulties.
Her first acting role was in 1946, a radio voiceover at the age of 10. Her first TV role came in 1954 in the TV movie A Nest Of Singing Birds.
The Glasgow University arts graduate then went on to star in many TV, radio and theatre productions.
In 1983 she won a Sony Award for her radio acting in a performance as Jean Armour in Till A' The Seas Run Dry.
Riggans is survived by her daughter Samantha and a grandson.
Bobby Hain, director of channels at STV, said: "We are very sorry to hear of the passing of Mary Riggans who was a much-loved actress and a popular cast member of Take The High Road.
"Take The High Road remains one of the longest-running drama series in the UK and Mary played a key part in its success."
Actress Julie Wilson Nimmo, best known for playing Miss Hoolie in Balamory, said: "I'm shocked and saddened to hear about Mary's passing. We worked together for years. She was a brilliant actress and will be remembered fondly by the Balamory family."
BBC Scotland executive Yvonne Jennings, who was a producer on Balamory, said: "As Suzie Sweet in Balamory, Mary was well respected by those who worked with her and much loved by the CBeebies audience.
"Like Suzie, Mary was a kind and giving woman who took on the role of nurturing young talent. She was an extremely professional actress with impeccable comedy timing. She'll be sadly missed by many."