During a stand-up gig on Sunday 6 November, the 41-year-old comedian allegedly said his girlfriend had just had a baby.
A fan at the show, known as Russellbrand-fancast on Twitter, tweeted: “Anyone else know Russell’s fiancée has had the baby?” alongside a photo of Brand.
When someone tweeted back asking for details, the fan replied: “Sadly he didn’t give any more information than his girlfriend has just had a baby.”
Another fan, Daniel Crann, 29, who was also at the show, told Mirror Celeb: “He was conscious of the clock.
“He made sure he was off stage by just approaching 9pm as he ‘needed to get down the f***ing M21 as my girlfriend has just had a baby’.”
People have taken to Twitter to congratulate the couple.
Russell Brand has previously said he is not going to “impose” a gender on his child when they are born.
“‘Jesus Three’ I’m thinking of calling him or her, we don’t know the gender, I may not even ever impose a gender upon it,” he said on the Jonathon Ross show on Saturday 15 October 2016.
“Let the child grow up and be the whatever the hell it is, never tell it there is such a concept.”
Brand and Gallacher announced they were expecting their first child together in May 2016.