The singer revealed last August that she had been diagnosed with breast cancer, which had spread to other parts of her body.
On Sunday, her mother Marie announced the death on Instagram, saying her “beautiful” daughter was “a bright shining star”.
Cheryl, then Cheryl Tweedy, was part of Girls Aloud with Harding, Kimberley Walsh, Nadine Coyle and Nicola Roberts from their formation on TV show Popstars: The Rivals in 2002.
Read more: Sarah Harding's 12 greatest moments
Sharing a black-and-white portrait of Harding on Instagram, she wrote: “Although we knew this day would arrive I am somehow still feeling at a loss for words that our stunning, unique, crazy, quirky, kind and soft-hearted girl has departed.
"As I try to navigate my way through these painfully strange and horribly unfamiliar waves of disbelief & finality I am experiencing, I wanted to extend my condolences to all of our GA fans.
“We were like an extended family for so long and we know so many of you by name.
“I wanted to make sure you knew just how much your love and continued support meant to Sarah through her most vulnerable times.
Watch: Sarah Harding 'fought incredibly hard'
“She was so grateful and you really lifted her spirits when she needed you most.
“I also realise so many will be deeply affected by the circumstances of Sarah’s passing… I am sending you all so much love. I love you Sarah… farewell.
“Sarah Nicole Harding forever in our hearts.”
Walsh also paid tribute on Monday, writing: “Beautiful Sarah this hurts so bad.
“To wake up and know that you are really gone is too much to bear.
“Hearing your infectious chuckle was one of my favourite things in the world.
“Your fire burned so bright and you loved, lived and laughed so hard.
“Sending love and strength to everyone who is grieving today.
“My heart is broken.”
Roberts also shared a series of photos of them together during Girls Aloud’s early years and wrote: “I’m absolutely devastated and I can’t accept that this day has come.
“My heart is aching and all day everything we went through together has raced round my mind.
“Especially this last year since her diagnosis, as hard as the year has been, our new memories are strong in my heart.
“There are so many things to say and at first it felt too personal to put them here and then I remembered that there are so many other people grieving her too.
“A part of me or us isn’t here anymore and it’s unthinkable and painful and utterly cruel.
“She would have loved your messages today.”
Roberts described her bandmate as “Electric girl” and added: “You gave it everything and still with a smile.
“A white butterfly flew past my window this morning before I knew, it must have been you.”
Coyle posted a photo on Instagram of Harding smiling broadly and said she was “absolutely devastated” by the news.
She added: “I can’t think of words that could possibly express how I feel about this girl & what she means to me!!
“I know so many of you will be feeling this way. For now I’m sending so much love to you!!!”
Harding’s mother announced her death on Sunday with a message which said: “It’s with deep heartbreak that today I’m sharing the news that my beautiful daughter Sarah has sadly passed away.
“Many of you will know of Sarah’s battle with cancer and that she fought so strongly from her diagnosis until her last day.
“She slipped away peacefully this morning.
“I’d like to thank everyone for their kind support over the past year.
“It meant the world to Sarah and it gave her great strength and comfort to know she was loved.
"I know she won’t want to be remembered for her fight against this terrible disease, she was a bright shining star and I hope that’s how she can be remembered instead. – Marie x”
Music manager Louis Walsh, who helped create Girls Aloud, said he would remember Harding with “great fondness”.
In a statement, he said: “It’s just sad she has gone too young. She was always fun and the life and soul of the party.
“Anytime she came to Dublin in the early days we went out to the Pod nightclub and would be the last to leave.
“It’s just so unfair, I was hoping she was getting better.
“She was fun and loved music, dancing and life.
“I will remember her with great fondness.”
Geri Horner, of the Spice Girls, who was also a judge on Popstars: The Rivals, wrote on Twitter: “Rest in peace, Sarah Harding.
Rest in peace, Sarah Harding. You’ll be remembered for the light and joy you brought to the world. X
— Geri Horner (@GeriHalliwell) September 5, 2021
“You’ll be remembered for the light and joy you brought to the world.”
Former Big Brother host Davina McCall wrote: “So so sad to hear about Sarah … a star from the get go, hugely fun and outgoing yet also somehow fragile … love to her family and friends.”
Earlier this year, Harding said she was told by a doctor that she would probably not be alive next Christmas.
In an extract from her memoir, titled Hear Me Out, which was published in the Times, she wrote: “In December my doctor told me that the upcoming Christmas would probably be my last.
“I don’t want an exact prognosis.
“I don’t know why anyone would want that.
“Comfort and being as pain-free as possible is what’s important to me now.”
Harding said she was “trying to live and enjoy every second of my life, however long it might be”.
“I am having a glass of wine or two during all this, because it helps me relax,” she added.
“I’m sure some people might think that’s not a great idea, but I want to try to enjoy myself.
“I’m at a stage now where I don’t know how many months I have left.
"Who knows, maybe I’ll surprise everyone, but that’s how I’m looking at things.”
Harding said that publicly revealing her diagnosis was “scary” but also “the right thing to do”.
She said the support she received had been “incredible”, adding: “I’ve been inundated with lovely messages from my fans.
“I’m grateful beyond words for that.”
Watch: Nicola Roberts pay tribute to bandmate Sarah Harding