A new survey found 58 per cent of graduates from Strathclyde University, in Glasgow, wanted to get a job in Scotland, while the same was true of 39 per cent and 31 per cent from the universities of Glasgow and Edinburgh respectively.
Most universities see much lower proportions of students seeking a job close to where they study, with a national average of just 24 per cent.
However, just 13 per cent of graduates from St Andrews University, in Fife, said they were planning to stay in the region to find work. The largest graduate population staying close to their institutions after graduating was in London.
Alastair Sim, director of Universities Scotland, said: "Our higher-education institutions not only nurture talented students and produce highly skilled graduates and postgraduates, they also generate world-class research and development and help create the conditions that make Scotland the most attractive place for businesses to invest in the UK, second only to London.
"This in turn ensures that there is a healthy graduate jobs market in Scotland which attracts the best talent and opportunities."
Overall, the survey by High Fliers Research found almost half of students start job-hunting by the end of their first year of university rather than waiting until the months before graduation.
Across the UK, a quarter of students said they expected to start a full-time graduate job as soon as they finished their studies.