Anne, who played Deirdre Barlow in the ITV1 soap for more than 40 years, passed away aged 60 after what her family have described as a battle with "short illness".
Overnight, hundreds of messages began pouring in on social media while the cast and crew posted a tribute to the legendary actress on the official Corrie website.
Leading the statement, executive producer Kieran Roberts said: "There are no words to describe the sense of grief we feel at Anne's passing.
"We know only too acutely how much Anne meant to the millions of people who watched her create the legendary character of Deirdre Barlow.
"She will be greatly missed by the Coronation Street team who share happy memories of working with her. We feel blessed and honoured to have known her. Our thoughts are with David and their family."
Meanwhile, William Roache - who played Anne's on-screen husband Ken Barlow - released his own statement, saying: "I feel Anne's loss so personally having worked closely with her for over 40 years. She was such a loving and vibrant person.
"You always knew she was there because her laugh was never far away.
"She was an impeccable performer with superb comedy timing and an immense gift for really heightened drama."
He added: "We had some rows over the years as Ken and Deirdre and it was wonderful to play those scenes opposite her. Coronation Street has lost one of its iconic characters and Anne will be greatly missed."
Beverley Callard took to Twitter to pass on her condolences, tweeting: "My beautiful darling friend, Anne Kirkbride, passed away in a room filled with love. God Bless, my Darling Girl! Peace and rest!"
My beautiful darling friend, Anne Kirkbride, passed away in a room filled with love. God Bless, my Darling Girl! Peace and rest!— Beverley Callard (@Beverleycallard) January 19, 2015
Michelle Keegan, who left Corrie last year after playing Tina McIntyre for six years, added: 'So so sad. Devastating news. Love you Annie. The nation is now in mourning..."
And it's not just Coronation Street actors and actresses who have been sending their wishes.
EastEnders' Jake Wood said: "My thoughts go out to Anne Kirkbride's family at this time. TV legend who forever made her mark, will be missed by many #CoronationStreet."
Co-star Natalie Cassidy added: "Sad sad news about Anne Kirkbride - A Coronation Street Legend. Soaps wouldn't be around if wasn't for people like Anne. God Bless. X."
Anne was last on screen in October and she was due to return to the soap next month.
She leaves behind her husband David, her brother John and his family.
Twitter tributes to Anne Kirkbride from her co-stars:
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