The You First scheme, which is run by the charity Barnardo's, was judged to be good at helping parents change their behaviour in practical ways, by teaching skills such as baby first aid and encouraging them to read and sing with their children.
However it was less successful with tasks more dependent on written skills, such as promoting budgeting and financial capability.
The authors stressed that the benefits of the programme would partly be long-term, through giving parents more confidence and encouraging them to interact more and spend more time with their babies.
You First offered help to parents aged 21 and under with a child under the age of one who live in the 15% most deprived areas in Scotland. The report says it was successful in working with parents other services find hard to reach.
Families from East Lothian, Midlothian and West Lothian – who volunteered to take part –were offered a 20-week programme focusing on child development and parenting skills.
You First is funded by the Scottish Government, and ministers also commissioned the research.
The Government said young parents had benefited in three main ways: through greater interaction with their babies, by developing a social network and through increased confidence in their abilities as parents.
Researchers said the programme had also led parents to have increased educational goals, and encouraged some to make the decision to seek work.
Minister for Public Health Michael Matheson, pictured, said the impact of the programme was positive and significant: "We are committed to giving every child the best start in life. Innovation and inspiration have a part to play and it is through projects like this that we are able to do so," he said.
The programme has already been expanded and now offers support to young parents across eight health board areas, Inverclyde and Renfrewshire, Lanarkshire, Forth Valley, Ayrshire and Arran, Tayside; Grampian and Highland.
Martin Crewe, Barnardo's Scotland director said: "We are delighted with the report. Since the expansion of the programme in 2011 we have been able to offer support to an additional 200 new parents and their babies. The first years are the most important of a child's life and it is vital that we all work together to give young parents the support they need.
"Barnardo's Scotland believes that young parents want to do the best they can for their children – they just need to be given the support to do it."