New statistics show 97.7 per cent of students from Robert Gordon University, in Aberdeen, found employment or continued with their studies after graduating in 2012/13.
The figure is the best in Scotland, and exceeded in the UK only by three London institutions: London University's Institute of Education, the Royal College of Music, and the Trinity Laban Conservatoire of Music and Dance.
Originally founded in Aberdeen in the 18th century as a hospital to care for and educate the poor, Robert Gordon achieved university status in 1992.
Its principal, Professor Ferdinand von Prondzynski, said: "We work closely with employers at all stages of the student journey, from course development and accreditation to providing scholarships and work-based placements and experiences. In this way we produce graduates that employers want."
Other Scottish universities that performed well, according to figures from the Higher Education Statistics Agency, included Edinburgh Napier University, where 95.4 per cent% of graduates went on to so-called positive destinations, Aberdeen University, where the figure was 95.3 per cent, and Glasgow Caledonian University, where 94.8 per cent of graduates secured a job or further study.
Overall, 93.7 per cent of graduates from Scottish institutions went into employment or further study.
Last week it emerged students from Scottish universities were more likely to get a graduate-level job when they leave than their counterparts across the UK.
Alastair Sim, director of Universities Scotland, which represents university principals, stressed the importance now placed on making graduates employable.
He said: "This is strong evidence that Scotland's higher education institutions produce graduates of the highest abilities, capabilities and are armed with a developed set of skills that employers require.
"Taken together with recent statistics on employment, these results provide a robust and compelling picture of the strength of employability measures that Scottish universities provide for their students and graduates, which will provide them with the best possible opportunities for their future careers."
Meanwhile, new figures show showed every council area in Scotland has seen a decline in the rate of its young people classified as not in employment, education or training. This continues a trend that has been apparent since 2008.
Angela Constance, Cabinet Secretary for Training and Youth, said it was "very welcome news".