Leeds-born Mellor, who was also best known for penning series including Fat Friends which aired from 2000 until 2005 and was turned into a musical, died on Sunday.
A spokesperson for her TV production company, Rollem Productions, said: “It is with profound sadness that we announce the untimely and sudden passing of our beloved friend, mentor and colleague Kay Mellor on Sunday 15th May 2022.
“We have lost a phenomenal talent and a true luminary. We ask that you please respect the privacy of the family and friends at this time.”
She began her career writing plays, worked on Coronation Street and created the award-winning children’s drama Children’s Ward.
She also wrote BBC One’s women’s football series Playing The Field and in 2010 received an OBE.
Bafta-nominated series Fat Friends focused on the members of a slimming group in Leeds, and starred James Corden, Ruth Jones, Alison Steadman and Mellor’s youngest daughter, Gaynor Faye.
Faye has also starred in Coronation Street, Emmerdale and The Chase on BBC One, a series which she co-wrote with her mother.
Mellor appeared on BBC Radio 4’s Desert Island Discs in 2017 and chose The Beautiful South’s Perfect 10, the Fat Friends theme tune, as one of her sound tracks, saying “every time I heard that I used to get excited and get butterflies”.
She explained: “It was such a lovely time of my life, it was a drama that was really important to me because I thought I had something to say about weight and body image.”
The BBC’s chief content officer, Charlotte Moore, said in a statement: “I’m shocked and deeply saddened to hear that Kay Mellor has suddenly passed away.
“Kay was an outstanding writer and the creative force behind many of the nation’s best-loved television dramas.
“She wrote with such heart, humanity, humour and passion with strong female characters often taking centre stage.
“She will be missed and our thoughts are with her friends and family at this difficult time.”
Mellor and her husband Anthony were married in 1968 and have two daughters, actress Faye and television producer Yvonne Francas.