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The Liverpool footballer's wife gave birth to a girl at 4pm this afternoon (Tuesday), weighing 7lbs, 15oz.
Both practising Catholics, they named the girl Lourdes after the French town to which pilgrims travel every year.
In a statement, a spokesman for the couple said that the baby is "doing well", adding: "Steven and Alex would like to thank the media for respecting the privacy of their family at this time."
The Gerrards, who married in 2007, have two older daughters - 7-year-old Lilly-Ella and 5-year-old Lexie - together.
News of Alex's pregnancy was revealed in May.
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