Baby Gabija was delivered to her Latvian-born parents Irene and Darius Smulkstiene at 12:03am at the Southern General Hospital in Glasgow yesterday.
The hospital said both mother and daughter, who weighed 7lb 9oz, were doing well.
The couple from Glasgow, were due to take their extra Christmas gift home later yesterday.
The birth came just one minute before a boy was born at the Princess Royal Maternity Hospital in the city.
Edinburgh’s first hospital delivery came hard on his heels at 12:05am, when Aleasha Campbell and Steven Todd from Edinburgh welcomed their daughter Lily into the world. She weighed 7lb 10.5oz.
In Elgin, Kelly Simpson was celebrating the arrival of Kianna at 1:08am – who now shares her birthday with her great grandmother, Carole Mitchell, 72.
Ms Simpson’s fourth child was born at Dr Gray’s hospital in the town, weighing 6lb 4oz.
The 23-year-old, who lives with her RAF engineer partner Duncan Kehoe, 24, in Forres, said her arrival had been a surprise because she was not due for nearly two weeks.
She said: “Funnily enough, I took my three children to see Santa on Friday. He asked me what I would like for Christmas and I said, ‘I would like my baby’, so I think I met the real Santa.”
Aberdeen Maternity Hospital’s first Christmas baby was 8lb 12oz Lucia, born to Gisella Gordon and her husband Jamie, both 36, at 1:22am.
The first baby to be delivered on Christmas Day at St John’s Hospital, at Livingston in West Lothian, was a boy weighing 9lb 10oz. Jacksen was born to parents Heather and Derek Brown, from Bathgate, at 2:22am. An hour and 20 minutes later, James Rogers arrived at 3:43am at the Royal Alexandra Hospital at Paisley in Renfrewshire, weighing 8lb 3oz.
However, there are pros and cons to having a Christmas baby, according to Borders’ mother Rachel Hunter.
Ms Hunter, 47, who gave birth to Jack on Christmas Day 13 years ago, said his arrival brought back special memories every year, but the date had proved tough for her son.
The museum consultant from Peebles, said: “I love the fact he was born on Christmas Day – it was a fantastic present. Every Christmas, it takes me back and adds an extra buzz to the occasion.
“However, we cannot have a full-blown birthday party for Jack – it’s just not possible to compete with the festivities.
“We can’t ask people to leave their families to join us, but we still mark his birthday with a cake and separate set of presents, and have a party in the summer.
“When Jack was younger he didn’t seem bothered, but now feels he’s been diddled.”