Graphic Design student Leanne Young won the competition with a forest fairy tale design featuring Highland cows, squirrels and the Loch Ness Monster.
It will feature on boxes to be given to every newborn baby from this summer until March 2019.
More than 70 students applied for the design competition, being run by the V&A Dundee, to decide what the boxes will look like.
One other design, by Marwa Ebrahim from Glasgow School of Art, was also highly commended by the judges.
The boxes, which are being piloted in Clackmannanshire and Orkney, will contain items including bedding, clothing and toys.
Ms Young, from Edinburgh Napier University, will receive a prize of Â£1,000 and "exclusive mentoring" from leading Scottish designers Holly Fulton and Scott Jarvie.
She said she was delighted her design would feature on Scotland's first baby box.
"I have thoroughly enjoyed the experience from concept to realisation and hope that young families will interact with the design I have created," she said.
"It's really exciting to be involved with the entire process and I've appreciated all the support and encouragement I have received from my mentors so far.
"The course at Edinburgh Napier has allowed me to develop my graphic design skills and allowed me to participate in this exciting new government initiative."
Judges praised Ms Young's high contrast illustration which they said was "visually stimulating" for babies. The images can also be customised by each individual family.
Early Years Minister Mark McDonald said: "It was an extremely difficult task trying to pick an overall winner but the judges were in agreement that Leanne's concept should be the first ever design for Scotland's baby box.
"Not only is it incredibly interactive, allowing families to customise and decorate the box throughout the years, it also acts as a multi-purpose memory capsule. It has space to record key milestones, a family tree and even the baby's handprints or footprints.
"Although all babies born in Scotland will receive one of these boxes I am extremely pleased that each one will be completely unique to every family."

The drama follows a slew of dramatic interest in the heist, after two films and a radio play about how the thieves broke into the vault.
Larry Lamb and Phil Daniels starred in a big screen version released in April, while Michael Caine and Ray Winstone will star in another upcoming film.
A cartoon also appeared on the BBC News website last year.
Six men were jailed for up to seven years for stealing items from the vault in central London in 2015, with an estimated two thirds of the valuables still unrecovered.
The robbery took place in London's diamond district, carried out by a gang of career criminals who drilled three 25cm holes through a concrete wall to climb into the vault.
Spall, who won best actor at the 2014 Cannes Film Festival for Mr Turner, will star alongside Kenneth Cranham in four 60-minute episodes.
Jeff Pope, ITV Studios' head of factual drama, said: "This is one of the most high-profile crimes of the last decade and we wanted to understand what had happened - and why it had happened.
"The research threw up some fascinating detail and blew away many of the misconceptions about this story. It was not about a bunch of 'loveable old blokes', many box holders lost everything in the raid and we will reflect this.
"But the planning was clever and the characters involved unique."
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The winning design for Scotland's baby boxes has been revealed.
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Timothy Spall is to star in ITV's dramatisation of the Â£25m Hatton Garden safety deposit box jewellery raid.