Students living in Wales will not have to pay top-up fees at Welsh universities under a new deal to break political deadlock.
English students would pay more than their Welsh counterparts
It means students from outside Wales would pay £3,000 from 2007, while their Welsh counterparts would pay £1,200.
The opposition said Labour had agreed to fill the funding gap between Welsh universities and the rest of the UK.
The Labour assembly government said it was pleased the "cloud of uncertainty" would be lifted as soon as possible.
The opposition had united in the assembly to vote against top-up fees in Wales, defeating Labour, which has lost its working majority in Cardiff Bay.
That vote was despite a report which recommended letting Welsh universities charge up to £3,000, the same as those in England will be able to do from 2006-7.
Since then the four party leaders have been holding talks to try to find a way ahead.
The opposition parties - Plaid Cymru, Conservatives and Liberal Democrats - now say they have won a promise that students living in Wales would be exempt from top-up fees.
They also said they had won a commitment from Labour to ensure Welsh higher education institutions will be funded to a similar level as their English counterparts.
'Forced to listen'
The assembly government said on Tuesday: "We are in the finishing straight.
"The four party groups have met to discuss the paper prepared by the party leaders. More discussions will occur to finalise the details of a motion to be tabled later today and debated tomorrow."
The new deal will have to be rubber-stamped by AMs in a vote.
Currently, students in Wales pay a flat fee which is expected to be £1,200 in the next academic year.
The deal will also see the introduction of a national bursary scheme - including incentives to study shortage subjects like maths and engineering.
Ieuan Wyn Jones, leader of Plaid in the assembly, said it was a very significant step forward which should "encourage a higher number of Welsh students to stay in Wales and will not offer incentives for English students to come here to avoid paying top-up fees."
Conservative Nick Bourne said Mr Morgan had been "forced to listen," and was a victory "for the will of the assembly."
A commission led by Professor Teresa Rees called for fees in Wales
Liberal Democrat Mike German said: "Welsh students will not have to suffer for being from a poorer background and face a mountain of debt before they start their working lives.
"This is a significant shift in the thinking of the Labour Party," said Mr German.
The acting president of the National Union of Students for Wales, Andrew Wilson said: 'We're glad to hear that the Assembly Government have made this commitment to Welsh students.
"However, it must be backed up with adequate student support to give students the means to live while they are studying.
'We've also got to remember that Welsh students make up less than half of the student population in Wales, so there is still a large group of students who will be paying the full amount."
Welsh universities had warned that they could suffer while they wait for the fees deadlock to be resolved.
Higher Education Wales, which represents Welsh universities, claimed it could lead to a brain drain of staff.