The 8lb 13oz bundle of joy arrived at the LGI at 6.21am on Christmas Day, 16 hours after mum Charlotte Sinclair went into labour on Christmas Eve.
Eliza, who is the first baby for Meanwood parents Charlotte, 31, and Matt, 35, has been given the middle name Pauline in tribute to her paternal grandmother, who died last year.
Charlotte said: “She is lovely and has been a dream so far.
“The midwives at the LGI have been fab and there was lots of Christmas spirit - people dressed up with tinsel and volunteers bringing crocheted gifts for the babies. We even got Christmas dinner.”
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Dad Matt added: “She is the best Christmas present ever.”