All Scottish universities have set tuition fees for students from other parts of the UK, with some charging £36,000 for a four-year degree.
Students resident in Scotland will not pay, but SNP ministers decided to bring in charges to protect places.
The decision to allow English universities to charge up to £9,000 for tuition sparked concern over "fee refugees" heading to Scotland.
A number of Scots universities will cap fees at the English level of £27,000.
Fees will apply to English, Northern Irish and Welsh students from 2012-13, although the rates will not become official until the outcome of a Scottish government consultation and new legislation is brought in.
The Scottish government put the estimated average annual fee at £6,841 - slightly higher than the £6,375 previously predicted, but less than the £8,509 average figure for England.
Scottish Education Secretary Mike Russell says he has reluctantly decided to allow universities to charge fees, saying Scotland must maintain its reputation for quality in higher education, rather than becoming seen as a "cheap option" to study.
However, the NUS says Scotland is set to become the most expensive place in the UK to study, with charges in some places of up to £36,000, compared with £27,000 in England, because many degrees offered north of the border take four years to complete.
Mr Russell, said: "Scottish students and their parents have long had the reassurance of knowing that undergraduate education in Scotland will remain free.
"To maintain opportunities for our students, and to protect our world leading universities' reputation and competitiveness, we had no choice but to respond to the increase in tuition fees to £9,000 south of the border."
The education secretary added: "I am pleased the majority of our universities have shown restraint and we estimate that the proposed average fee of £6,841 will be further decreased by packages of bursaries and fee waivers to around £6,375."
Edinburgh and St Andrews universities, as well as the Royal Conservatoire of Scotland are to charge £9,000 a year, making the cost of a degree as much as £36,000.
Other institutions, such as Edinburgh's Heriot-Watt University and Glasgow School of Art, want to charge £9,000-a-year, but will cap fees at £27,000 for four-year courses - essentially giving students one free year.
And some, such as Stirling University and the Scottish Agricultural College, want to charge £6,750 per year, also putting the cost of a four-year degree at the £27,000 English level.
Some universities also offer some students the option of direct entry to the second year of a course, while there is an ongoing debate over a wider move from four to three-year degrees in Scotland.
And a new range of bursaries, available to all students, is to be introduced in 2012.
The introduction of £9,000-a-year tuition fees in England, shepherded in by the UK government in light of the public spending squeeze, has proven highly controversial.
In Scotland, upfront tuition fees were ended in 2001 and their successor - the £2,289 graduate endowment - was scrapped in 2008.
The Scottish government is moving forward with a consultation on legislation allowing universities to set their own fees for students from the rest of the UK from 2012-13.
The move would then be followed by new legislation to cap fees at £9,000 a year from 2013-14 onwards.
Scottish universities were given the option of setting fees as low as £1,800 and Mr Russell previously said he expected levels to be lower than those south of the border.
Opposition parties in Scotland - Labour, the Liberal Democrats and Greens - have backed the SNP's position to keep university education free for Scottish residents.
But the Scottish Conservatives have questioned the legality of the fees plan, and say it could stir up resentment in the rest of the UK against Scotland.
Elsewhere, the Scottish government is seeking an end to rules where it has to pay the fees of students living in non-UK EU countries, which it says is costing the taxpayer £75m a year.