The study, by Carnegie UK Trust, showed 51% of people aged 15-24 used libraries in 2016 - an increase of 9% since 2011.
Overall, there has been an increase in public library use, from 45% to 46% over five years.
Northern Ireland has also seen its library use go up, but there have been declines in England and Scotland, the wellbeing trust said.
The findings are based on 10,000 interviews conducted in 2011 and 2016.
The trust said there was also a jump in library use in households with pre-school children (7%) and primary age children (3%).
Chief executive Martyn Evans said: "Public libraries remain an immensely popular civic resource, both in Wales and across the rest of the UK and it's extremely promising that there's been a rise in library use in Wales amongst households with pre-school and primary children, as well as young people."
More than half of young people in Wales use public libraries, research has shown.