An average of 1,000 baby boxes per week were delivered to parents of newborns in the first year of the programme.
The Scottish government said 52,065 baby boxes had been gifted to date, with an 85% uptake by parents.
The boxes contain items including clothing, a play mat, books, a towel and a sling carrier – and the box itself can be used as a sleeping space.
The projected cost of the initiative was £8m for 2017-18, rising to £8.8m for each of the following three years.
The Museum of Childhood in Edinburgh has announced that one of the boxes is to be exhibited in the museum from next year.
Sandra Martin, history curator for Edinburgh’s Museums and Galleries, described the boxes as a “great equaliser”.
She said: “The museum houses some extraordinary examples of childhood history from all sides of Scottish society.
“From real silver spoons, a popular gift with babies in Victorian Edinburgh, to makeshift dolls crafted with nothing more than a wooden spoon and some old cloth, by families who couldn’t afford anything more.
“The modern baby box is the great equaliser. The same gifts for baby, available to all new mothers. It’s a pleasure to welcome it into our collection.”
Children and Early Years Minister Maree Todd said that they were having a real impact on the families receiving them, and demonstrated that “as a society, we value each and every child”.
Ms Todd said: “I’m delighted to have reached this milestone.
“It’s an honour for everyone involved – from the organisations providing the items to the box packers to the people delivering the boxes – to have been part of something that is having a real impact on the lives of babies and their carers across the country.”
A parent survey revealed the most popular items were the room thermometer, followed by the ear thermometer and the sling.
The majority of parents (62%) said they had used or planned to use the box as a bed.
The Royal College of Midwives recently backed the introduction of a similar scheme for the whole of the UK.