Antony announced the news on Twitter last night (24 June) along with a picture of a pink babygro emblazoned with the words 'Daddy's No 1 Girl'.
Alongside the snap, the Big Reunion star told his followers: "Your first breath, took ours away. Welcome to the world our beautiful little girl."
Antony's Blue bandmate Duncan James were quick to congratulate the couple on their baby news.
The dad-of-one said: "So happy for @AntonyCosta and @RosannaJasmin for the birth of their lill girl. Another blue baby - we gonna have our own band of kids soon!"
The official Blue Twitter account also posted: "Join us in wishing @AntonyCosta & @RosannaJasmin all the very best as they celebrate the birth of their daughter. A very special moment .."
In December, Antony got engaged to dental nurse Rosanna Jasmin during a romantic trip to Paris.
A week later, the couple announced that Rosanna was pregnant with their first child together.
Antony is already a dad to daughter Emilie, who he fathered with his ex-fiancèe Lucy Bolster in 2003.
Celebrities who have welcomed babies in 2014:
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