Around 300,000 Australian babies are currently born each year, meaning the bank could give up to A$60 million ($62.6 million).
Westpac Group's consumer banking chief executive George Frazis said helping children to start saving early could pay off in later years, setting them up with good financial habits.
"By building on an initial $200 deposit at birth with a $20 contribution every week, for example, will potentially amass approximately $19,000 in savings (based on a 1.5 per cent interest rate) by the time the child turns 16," Frazis said.
"That's a significant financial head start for any child and can be put towards future education, life experiences such as a gap year or a deposit on a first home," he said.
"We've listened to parents and grandparents and believe the Bump Savings account will demonstrate the benefits of long term savings to young people, so by the time they turn 16, they might consider continuing to save their money."