The couple, who already are proud parents to 3-year-old Amelie, shared their excitement within hours of the birth.
Alex announced the birth of their healthy 7lb 7oz baby on Twitter, writing:
'Delighted to announce the safe arrival of our gorgeous little girl. @msrachelstevens and baby both really well. Amelie happy and excited.'
The couple later released am official statement, revealing:
'We are so happy that baby has arrived safely. Within minutes of meeting her we're completely smitten.'
They added:
'Amelie is happy and excited to have a little sister to play with and we can't wait to introduce her to the whole family.'
The S Club 7 star announced her pregnancy on Twitter in September, writing:
'Alex and I are so happy to find out we are pregnant again and can't wait to meet our new little member of the family early next year. Needless to say we're all super excited, especially Amelie who is looking forward to meeting her new brother it sister.'
The couple kept the sex of their second child a secret from friends and family, until the birth yesterday.