The figures from the Universities and Colleges Admissions Service show that 4,039 students from England had been accepted on to courses in Scotland as of 22 August, up from 3,197 at the same point in the admissions cycle last year.
There has been a similar percentage increase in the number of Welsh students taking up places in Scotland, although from a much lower base - up to 109 acceptances from 86 last year.
While Scottish students studying in their own country do not pay tuition fees, those from England will be charged up to £9,000 a year this autumn.
The average fee being charged per year in Scotland is less than in England, but as Scottish degrees are generally four years long, studying in the country is likely to be more expensive overall than staying in England.
However, there has been speculation that students from the rest of the UK might find it easier to win a place at university in Scotland because they will come with more money attached than Scots.
Robin Parker, president of the National Union of Students Scotland, said it was important to keep an eye on how fee income from other UK students was being spent.
"We will...make every effort to ensure that any additional income from this new system is spent on the right priorities, with full transparency and accountability," he said.
The detailed statistics from Ucas also show that places being taken at UK universities by other European Union students have dropped by 13.7 per cent compared with last year.
In England, the fall was 17.4 per cent, with 14,539 students accepting places compared with 17,597 in 2011. Scottish universities and colleges saw a 2.5 per cent increase in acceptances from other EU students, while figures in Wales were virtually unchanged. In Northern Ireland, only 13 students from other EU countries had accepted a place, down from 46 in 2011.
Meanwhile, there has also been a large drop in the number of students from Northern Ireland accepting places at universities in other parts of the UK. Acceptances for students from Northern Ireland were down 19.1 per cent in England, .6 per cent in Wales and 19.1 per cent in Scotland.