Dame Barbara, 80, was diagnosed four years ago but her husband Scott Mitchell revealed the details publicly in an interview published on Thursday in The Sun.
Dame Barbara is taking medication to manage her condition.
However, her memory loss and confusion have grown worse in recent weeks, her husband said.
In the unpaid interview, Mr Mitchell told the newspaper: “Firstly, I hope speaking out will help other families dealing with loved ones who have this cruel disease.
“Secondly, I want the public to know because they are naturally very drawn to Barbara and she loves talking to them.
“So rather than me living in fear she might get confused or upset, they’ll know that if her behaviour seems strange, it’s due to Alzheimer’s and accept it for what it is.”
Recalling the moment when the couple were told of Dame Barbara’s diagnosis, Mr Mitchell said: “She began crying then held it back, stretched her hand out to me and mouthed: ‘I’m so sorry’.
“I squeezed her hand back and said: ‘Don’t worry, we’ll be OK.'”
Mr Mitchell said he was giving the interview because “I can’t protect her any longer” and “I know that rumours are circulating in showbusiness circles”.
He added: “And, since her 80th birthday last August, a definite continual confusion has set in, so it’s becoming a lot more difficult for us to hide.
“I didn’t want someone else to dictate how or when the diagnosis came out, so that’s why I’m speaking about it now.”
Mr Mitchell said he first noticed symptoms of Alzheimer’s in 2009, when Dame Barbara began finding it difficult to learn her lines.
By 2016, the forgetfulness and confusion were worse, and it was agreed she would leave EastEnders for the final time.
Barbara Windsor made her stage debut aged 13, but it was her roles in the Carry On movies that made her a star.
She appeared in nine of the films between 1964 and 1974.
Later a whole new audience came to know her as the long-time pub landlord Peggy Mitchell in Eastenders.
But since her stage debut aged 13, Dame Barbara has appeared in a number of roles, including in Dad’s Army, Worzel Gummidge and One Foot In The Grave.
She was awarded an MBE in the Millennium New Year honours.
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Away from her acting roles, Dame Barbara is probably most famous for her support of the Royal British Legion’s Poppy Appeal.
However, Mr Mitchell said his wife had now retired from charity work as well as acting.