It follows a similar move for the universities, announced last month.
Higher education activity in colleges represents a quarter of the total teaching time. Jack McConnell, as the First Minister, signalled the change in a speech in February.
Ministers were understood to be worried that their cherished target to get half of young Scots into higher education, both in FE colleges and universities, could be at risk if the cap was not lifted. The proportion has been steadily declining from a high of 51 per cent to 45 per cent.
Roger McClure, chief executive of the funding council, acknowledged that removing the restriction on full-time HE students in colleges could lead to an upturn in numbers.
The cap was imposed amid concern that the cash-limited budget of the Student Awards Agency for Scotland could be over-stretched. But experience has shown that colleges and universities have not exceeded the limits on HE numbers and the SAAS has not been placed under financial strain. The Scottish Executive will review the position in 2010.
The change was revealed in the annual grant settlement for the 2007-08 academic year, notified to all 43 colleges this week. They will receive pound;528 million, a 5 per cent rise. An additional pound;88 million will go towards capital building programmes.
Within the total, the amount provided for actual teaching rises by 4 per cent to pound;492 million, with some colleges receiving up to 6 per cent more. The largest pay-out of pound;33 million goes to James Watt College in Greenock and the smallest, pound;371,000, to Newbattle Abbey College in Dalkeith.
This year's grant round also includes a significantly increased funding of 36 per cent to support colleges in working with schools, bringing it to Pounds 18.8 million. The money will allow fees to be waived for pupils at college, help with training and development, and provide enhanced careers advice.
Colleges will get pound;7 million for key priorities - pound;3 million to target youngsters not in education, employment or training; pound;2 million to improve collaboration with employers and develop workforce skills; and pound;2 million for knowledge transfer. These sums will not be allocated until later in the year.
Mr McClure said he was pleased the funding council had been able to make "a modest start" on knowledge transfer work in colleges: "The universities have been doing this for years, but the realisation has been slowly dawning that colleges should be involved as well.
"For a start, there are a lot more of them, they are local and they are, therefore, well placed to work with small and medium-sized businesses, particularly at the low-tech end of the scale. This is not about high-tech innovations from the university research lab but support to develop expertise in SMEs."
The scope is vast: just over a quarter of a million companies employ fewer than nine people.
Unlike the universities, colleges will not get specific funding to stem drop-out rates. Instead of receiving pound;4.3 million as a widening access premium, the HE institutions will get pound;10 million next session.
Mr McClure said the council was more concerned with retention problems in HE than in FE. There is already an incentive for colleges to hold on to students, at least for part of the year, since they do not receive any council funds until students complete 25 per cent of their course. "If you're trying to encourage people to take part in lifelong learning who might not otherwise have thought of doing so, you don't discourage the movement of students in and out of college," he said.
The settlement also includes a 3 per cent increase for student bursary support, bringing it to pound;56 million. Colleges which take in fewer students than expected pay unspent bursary money into a central pool, around pound;1 million to pound;2 million, which the funding council allocates to colleges with more students than they anticipated.