She died peacefully in hospital yesterday, her niece Sonia Hearld said, reported BBC.
Alexander had been admitted to Southport hospital, Merseyside, for tests but was discharged after a couple of days and allowed to return to her nursing home, her niece said.
But on Tuesday she was readmitted to hospital, three days before her death.
Alexander portrayed Hilda Ogden, a sharp-tongued, put-upon housewife who was one of Coronation Street's best known characters, from 1964 to 1987.
She appeared as shopkeeper Auntie Wainwright, the "absolute favourite part" of her career, for 22 years.
Sally Dynevor, whose character Sally Webster first appeared in the soap in January 1986 almost two years before Alexander left, wrote, "Jean Alexander, RIP. What a wonderful woman, and such an amazing and talented actress."
Jennie McAlpine, who has played Fiz Brown since 2001, tweeted, "So sorry to hear about Jean Alexander. I would have loved to work with her. Thankful to have met her though. Rest in Peace Jean x."
Prior to her role as Hilda, Alexander had a brief appearance in Coronation Street in 1962 as a landlady who rented a room to a disturbed young woman.
Alexander left the soap in 1987.
She later joined "Last of the Summer Wine" in 1988 as the junk shop owner Auntie Wainwright, a role she would play for 22 years.
But Hilda Ogden was the character she remained best known for. In 2005, a TV Times poll voted her the nation's favourite soap character.
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