Barbara Windsor in Carry On Camping
Mitchell, who married the star in 2000, paid tribute to the "love, fun, friendship and brightness she brought to all our lives".
He added: "I've lost my wife, my best friend and soulmate and my heart or life will never feel the same without you."
Born Barbara Ann Deeks, in London's East End in 1937, she made her stage debut at 13 and went on to feature in her first film, The Belles Of St Trinian's, in 1954. She would go on to become a household name as a star of the Carry On films - although she only appeared in about a third of them - establishing herself as a classic "dizzy blonde" with a distinctive laugh, and though she continued to work both onscreen and stage, it did result in her suffering from typecasting.
Speaking of ageing out of that type of role, she said: "I found myself in the doldrums in the early 90s. I was too old to play the dolly bird any longer and I looked too young to play a woman of my real age."
Her career underwent a renaissance in the middle of that decade, however, when she took on the role of Peggy Mitchell, the landlady of EastEnders' Queen Vic.
Tributes have poured in for the star, who became a dame in 2016, two years after her Alzheimer's diagnosis.
Danniella Westbrook, who played her on-screen daughter Sam Mitchell in EastEnders, tweeting: "My heart is broken. Bar, you will always [be] in my heart forever."
Matt Lucas tweeted: "Everyone knew her and everyone loved her. She worked tirelessly for charity and continued to do so, even when her own health failed her."
And Elton John's official Twitter feed carried a picture of the singer with Babs, adding: "The world has lost the biggest ray of light. And heaven has the sweetest and funniest angel."
The Alzheimer's Society said: "Dame Barbara Windsor was an amazingly true, much-loved national treasure, and in speaking out about her experiences shone like a beacon for others affected by dementia."