From 2012-13, institutions north of the border will be able to charge other UK students up to ?9,000 a year in tuition fees, whereas Scottish and other European Union applicants will go free.
A teaching grant from the Scottish government will support those undergraduates, set at ?5,8 a year for low-cost subjects such as the humanities.
More money is allocated for students studying expensive courses such as engineering and medicine, but if fees from other UK students do not cover the required amount, Holyrood will make up the difference.
By contrast, rest-of-UK students will be charged an average of ?6,890 a year, potentially giving Scottish universities a greater financial incentive to accept such applicants on lower-cost courses.
However, only the University of Edinburgh has increased the proportion of offers it makes to UK students hailing from outside Scotland.
The number of offers made to such students was 5,828 compared with 3,494 at the same point in the applications cycle last year, according to figures obtained by THE.
An Edinburgh spokesman said that this was because other UK students are likely to have more offers to choose from this year, and because the number of Scottish and EU students that it can recruit is restricted by the Scottish Funding Council.
At the University of Glasgow, the University of Aberdeen, Edinburgh Napier University, Queen Margaret University, the University of Strathclyde, the University of the Highlands and Islands and the University of the West of Scotland, the proportion of offers made to rest-of-UK students has fallen, the figures show.
Other Scottish universities were unable to provide offer statistics in time for THE's deadline.