Mr Andrews said today that a detailed report published by the Higher Education Funding Council for Wales outlining a shakeup of the sector made a “persuasive case for change” and he accepted the “the broad thrust” of the recommendations.
Aberystwyth and Bangor universities have also been told to “develop a longer-term plan for merger”.
The Hefcw report accuses Welsh universities of being too numerous and too small.
Last December, Mr Andrews told Welsh universities to “adapt or die” and Hefcw has already said that the number of institutions should shrink from 10 to six, with no more than two in each region of the country.
Trinity Saint David and Swansea Metropolitan have been in talks since the beginning of the year, although the University of Wales Institute, Cardiff, pulled out of talks to join them earlier this month.
Since February, Bangor and Aberystwyth have been talking about a closer partnership, although John Hughes, Bangor’s vice-chancellor, said that they were too far apart to merge.
Glyndwr University has been asked to develop “strong structural relationships with a range of further education colleges within a group structure led by Aberystwyth and Bangor.”
The report also suggests that Glyndwr could share services with nearby University of Chester.
The Hefcw report also acknowledges that arguments over Welsh universities are far from new. “Debate on the structure of the higher education sector in Wales dates back to 1406, when Owain Glyndwr sought support from the King of France for the rebellion against the English and for a plan to create two universities in Wales,” it says.