The 33-year-old Blue star and proud new dad announced the happy news by posting a photograph of a pink babygro emblazoned with the slogan Daddy's No. 1 Girl on his Twitter page and wrote: "Your first breath took ours away. Welcome to the world our beautiful little girl."
Antony's Blue bandmate Duncan James was among the first to congratulate the couple on the new arrival.
"So happy for @AntonyCosta and @RosannaJasmin for the birth of their lill girl," he posted. "Another Blue baby - we gonna have our own band of kids soon!"
Antony, who recently appeared on The Big Reunion, proposed to Rosanna in Paris in December last year, getting down on one knee on her birthday.
He revealed they were expecting their first child together later that month, saying: "I’m going to be a dad with the love of my life. I am seriously the happiest I've ever been."
It is believed the couple will wed next year.
Antony and Jasmin, 28, have been excitedly sharing every detail of the pregnancy with fans. In January, they showed off their scan, with the caption: "The greatest adventure lies ahead".
Later they gave followers a peek of their 4D scan, which clearly showed the baby's features in the womb. In another image Rosanna's father was seen building the baby's crib.
Life has fallen into place for the pop pin up since he met Rosanna in a bar in Woodford, Essex, in June 2012. Antony has revealed that she encouraged him to give up drinking and lead a quieter life.
He said in an interview in April: "The last time I drunk was New Year's Eve. I don't need to any more. I'm in a relationship and I'm happy. Rosanna keeps me grounded and I don't need to go out partying."