Taylor-Wood, 43, a filmmaker and the 20-year-old British actor welcomed Wylda Rae to the world on Wednesday in London, their rep confirms to PEOPLE.
The couple, who met in 2009 on the set of her directorial debut, Nowhere Boy, raised eyebrows when they first stepped out together at a premiere earlier in the year. Taylor-Wood is already a mother of two from an 11-year marriage to art dealer Jay Jopling.
"I've got a wonderful woman," Johnson said in April. "I'm an old soul and she's a young soul."
Taylor-Wood also defended their age difference, telling Harper's Bazaar that judgment about their relationship is "totally sexist. I try to ignore it. I've made lots of big decisions in my life that have shocked people. I've never really thought of other people's opinions, so why start now?"
"It's just the outside world that feels they have to remark," she told the fashion magazine in its April issue. "And you can't listen to it."
• Reporting by SIMON PERRY
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