And the couple have exclusively revealed the new arrival's name to HELLO! magazine.
The baby girl, who weighed in at 7lbs 13oz, is called Aoife Belle Foden.
Aoife (pronounced Ee-fah) is a popular Irish name and traditionally means 'beauty'. Belle is the French adaption of Ben's mother's maiden name of Bell, and means 'beautiful' in French.
Ben broke the happy news of the birth on Twitter on Tuesday, writing: "I am officially a Dad!
"Una and baby are both amazing and healthy!!!! So proud of them both!"
Thirty-year-old Una's bandmates were quick to send their congratulations.
Vanessa White wrote "Congratulations @ben_foden @unahealy and baby! So happy!! Xxx"
Rochelle Wiseman said: "I'm proud of all 3 of you! Can't wait to be aunty x
"A beautiful girl has entered the world today and, I'm her aunty #blessed I'm so proud of @unahealy @ben_foden BIG love! Xx"
Also tweeting her love was Frankie Sandford, who wrote: "Congrats. So excited!!! Big hug... Don't forget Una on mothers day Sunday! How cool. Ur mum and dad! X."