The Iron Man star and his wife Susan welcomed a daughter earlier this week, according to a report in People magazine.
Robert had announced that they were expecting a baby girl in a message on his Twitter account. "Yo. Susan. Me. Baby. Girl. November. Scorpio?" he wrote.
They already have two-year-old son Exton together, while Robert is also father to 21-year-old Indio, from a previous marriage.
The couple hit the red carpet at the BAFTA Los Angeles Jaguar Britannia Awards just last week and Robert, who received the Stanley Kubrick Award for Excellence in Film, gushed about his wife during his acceptance speech.
"How is she so darn pretty and functional and mood stable," joked the 49-year-old. "This pregnancy has been extraordinarily tough for me - self-prescribed mandatory bed rest. There's some benefit, at least my milk is finally coming in."
Robert and 40-year-old Susan, a film producer, who met on the set of the movie Gothika have been married since 2005. Their son Exton was born in 2012.
The pair have production company together named Team Downey.
Representatives for the couple have not yet commented on the news.
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