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15 August 2018, 05:52 | Updated: 15 August 2018, 11:41
An average of 1,000 baby boxes per week have been delivered to parents of newborns in the first year of the programme.
The Scottish Government said 52,065 baby boxes have been gifted to date, with an 85% uptake by parents.
The latest survey showed 100% satisfaction with the box, which contains items including clothing, a comforter toy and a play mat, the government said.
Other gifts include books, a towel and a sling carrier, and the box itself can be used as a sleeping space for newborns.
The projected cost of the initiative was £8 million for 2017/18, rising to £8.8 million for each of the following three years.
Children and Early Years Minister Maree Todd said the baby boxes 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.
Darren Burt and Mandy Niblo from Falkirk said they were grateful for the digital ear thermometer they received in the box before their three-month-old Harris was born.
They said it would not have occurred to them to buy one, but it turned out to be essential when Harris got an infection. The high reading led them to call 111 and he was admitted to hospital, where he made a recovery.
Ms Niblo said of the box: "It's packed full of great quality, useful items including some that you might not think to buy yourself, that could potentially save your child's life."
NHS Lothian chief midwife, Frances McGuire, said: "The Baby Box has been a great opportunity for our midwives and health visitors to chat to expectant parents about its contents and how they can help improve a child's health and well-being.
"Not only that, but the box helps new parents at a time where they may be particularly stretched financially, and can provide crucial support."