The application rate for 18-year-olds from deprived areas is also the highest ever, with the 2016 data showing youngsters from this background are 65% per cent more likely to bid for a university place than they were a decade ago.
A total of 45,420 people in Scotland had submitted an application to Ucas by its January 15 deadline, a 1 per cent rise from the same point in 2015.
But applications from would-be students across the UK fell by 0.3 per cent, with this a result of a 1 per cent drop from England.
While the number of English students applying for a place at an English university fell, more want to come north of the border for their studies. By the deadline there had been 29,190 applications to Scottish universities from south of the border, compared to 24,310 in 2012.
A third (32.6 per cent) of 18-year-olds in Scotland have applied to go to university this year, according to the data.
While the application rate from 18-year-olds in deprived areas is at its highest ever at 16 per cent, this is lower than England (22 per cent), Wales (20 per cent) and Northern Ireland (24 per cent).
Education Secretary Angela Constance hailed the Ucas figures as being “further excellent news for Scotland’s university sector which saw record-breaking levels of applications and acceptances in 2015”.
She added: “A new record number of applicants demonstrates real ambition on the part of Scotland’s young people and underlines our global reputation for excellence in higher education.”
Ms Constance continued: “We have five institutions in the world’s top 200, more per head of population than any other country except Luxembourg. We are continuing to invest over £1 billion in the sector, to ensure it keeps punching above its weight on a global level.
“Scottish domiciled students continue to benefit from free tuition, a key part of our work to ensure access to higher education remains based on the ability to learn not the ability to pay.
“The Commission on Widening Access will present its findings in the coming weeks which will outline further ways to help even more students from disadvantaged backgrounds benefit from a degree education.”