First-time parents Tom and Eliza Lynch were yet to decide on a name for their little boy, who was born at 4am on February 29 in Wagga's Calvary Hospital.

Weighing 3.78 kilograms and measuring 48 centimetres, the little "leapling" arrived two weeks early, a date his dad predicted.

"At Eliza's baby shower, we had to guess the day the baby was born. I guessed the 29th, and here he is," the new father said.

"Hopefully he's got a better hairline than mine - it actually looks similar."

The Coleambally couple chose not to find out their baby's gender and wanted to see their bub before choosing a name.

Once they've chosen a name, the Lynches will also need to decide which day to celebrate their son's birthday - as the next time his birthday comes around will be in 2028.

"I'm born on February 23, so we will probably keep it [the birthday] on the 28th," Mr Lynch said.

"Eliza and I have been together for nearly 10 years, so it's exciting for the next chapter."

Karen Freemantle is a registered midwife at the hospital and said that what the couple now need most is a good sleep.

"They're pretty exhausted, as far as we're concerned we'll let them sleep and give them plenty of time and plenty of support," she said.

Ms Freemantle has worked as a midwife at Calvary Riverina Hospital for 21 years but says she hasn't had a baby born on the leap day before.

"Even though this birthday is pretty unique, every baby is extremely special and precious, the apple of their parent's eye," she said.

February 29 is the rarest birthday because it only occurs every four years.

In 2020, there were 568 babies born in Australia on this day.