According to Us Weekly, the Layer Cake actress welcomed a baby girl on Saturday (7th July), but offiical reps for the couple are still yet to confirm the reports.
Miller previously kept quiet about her expected arrival until well into her pregnancy and it was her step mum, interior designer Kelly Hoppen, who let the cat out of the bag in January.
At the time, she told London's Evening Standard: "Sienna is definitely not engaged or getting married, and she is pregnant."
Sienna, who had a long-running on-and-off relationship with actor Jude Law, then confirmed the news in British Vogue, telling the fashion magazine: "Even though I'm under strict instructions not to say anything as it would completely defeat the point of everything I've tried to achieve in the last eight years.
"I'm feeling fine… It's all progressing nicely and it's very exciting."
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