ITV confirmed the veteran performer's death in a statement on Friday night.
A spokeswoman for the programme said: "It's always sad to hear of the death of an actor who played a significant part in Emmerdale's success.
"Even more so when that actor was in the very first episode and around whose family the show was built.
"Annie Sugden embodied all the virtues of Yorkshire .... she was hard working, resilient, determined, down to earth and didn't suffer fools gladly.
"Sheila had many of those qualities too, putting the needs of the programme above her own and always delivering a great performance come rain or shine. She will be greatly missed."
King, who played the villainous Kim Tate on the ITV show, said: "RIP Sheila Mercier, the beating heart of Emmerdale, never forgotten, so many wonderful memories, love and condolences to all her family."
The prestigious British Soap Awards also remembered Mercier for her contribution.
A statement on Twitter said: "RIP Sheila Mercier. Emmerdale's original leading lady and the very definition of a matriarch
"Our thoughts are with her friends, family and the Emmerdale team tonight."
Mark Charnock, who plays Marlon Dingle, said: "The great #SheilaMercier has left us. What an iconic character Annie Sugden was.
"Used to watch it with my grandparents as a boy, so to meet her in later years was a thrill.
"I was star struck and she was so lovely to me. RIP."
Mercier was one of the first to join the soap when it launched as Emmerdale Farm in 1972, and appeared in the first episode.
She quickly became known for her portrayal of the matriarch Annie Sugden.
Mercier appeared between 1972 and 1994, and continued to make guest appearances in the following years.