Mellor, who wrote hit series including ITV's Girlfriends, Band Of Gold and The Syndicate and was also best known for penning hits including Fat Friends which aired from 2000 until 2005 and was turned into a musical, died on Sunday. (May 15)
Corden, who starred as Jamie Rymer in Fat Friends paid tribute to Mellor on Instagram, writing: "Kay Mellor sadly passed away today.
"She was the most generous, kind and loving person. An exceptionally gifted writer.
"She changed my life when she cast me in Fat Friends on ITV. She saw something in me that no one had before that point.
"She gave so many people their first chances. I have the fondest memories of being on set with her. She will be missed by so many.
"My thoughts are with her family and friends at this time x"
His tribute follows that of Welsh actress Ruth Jones, who also starred in Fat Friends and said British television has "lost one of its greats" after Mellor's death.
Jones, who played the role of Kelly Chadwick in Fat Friends, said in a statement to the PA news agency: "I am completely shocked to hear the news of Kay's untimely death. Her contribution to British television was outstanding and I feel privileged to have worked with her.
"Such a down-to-earth, funny, big-hearted person whose brilliance lay in seeing the extraordinary in the day to day.
"She was a great mentor to me when I first started writing - and always hugely encouraging of new writers - a real testament to the idea of paying it forward.
"Her series Fat Friends was a massive turning point in my career and I will be eternally grateful to her for what she did for me.
"British television has lost one of its greats. Thank you Kay for all that you gave us. I cannot believe you've gone.
"My thoughts are with Anthony, Yvonne and Gaynor and all the family at this unconscionably sad time."
A spokesperson for Mellor's TV production company, Rollem Productions, told the PA news agency: "It is with profound sadness that we announce the untimely and sudden passing of our beloved friend, mentor and colleague Kay Mellor on Sunday May 15 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."
Mellor 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 soundtracks, 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."
Band Of Gold, about a group of women from Bradford's red light district, starred Samantha Morton, Geraldine James, Fiona Allen and more.
Sir Lenny Henry, who starred in the third series of Mellor's hit TV series The Syndicate, based on a group of lotto winners, tweeted: "I was saddened to hear that Kay Mellor has died.
"I was lucky to work with her on The Syndicate and found her to be incredibly creative, funny and instinctive. She knew what she wanted and knew how to get the best from us as actors.
She will be missed. Condolences to her family."
The fourth series of The Syndicate aired in 2021 and was set between Yorkshire and Monaco and followed the workers at Woodvale Kennels, who were devastated to learn they may be out of a job when the owners announced they were selling the business to a large corporate chain.
The cast included Katherine Rose Morley, Kieran Urquhart, Liberty Hobbs, Emily Head, Neil Morrissey and Kym Marsh.
With previous instalments of the series set in a supermarket, a hospital and a crumbling stately home, Mellor shared how getting a dog had changed her life.
She told PA at the time: "I know that sounds mental but, actually, I love him so much. And I realised - maybe it's an English thing, I don't know - but we love dogs."
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."
ITV's director of drama, Polly Hill, also described Mellor as an "incredible writer of television, film and theatre" and "a director and producer who always managed to connect in a unique way with the audience".
In a statement, Hill added: "I was lucky enough to work with her many times at the BBC and here at ITV and she was an incredible woman, wonderful to work with and who I, like so many in our industry, will miss hugely.
"Kay will also be missed by the audience. I have been with her many times as she was stopped by people in the street telling her how much they love her characters, how they related to them and wanted more. Thank you Kay."
Mellor and her husband Anthony were married in 1968 and had two daughters, actress Gaynor Faye and television producer Yvonne Francas.