The university's council also said it intends to renovate the Pantycelyn accommodation.
But the council did say the necessary funding would have to be secured so it could give a definitive commitment.
Students have previously held protests over its proposed closure, calling for it to stay as a Welsh halls of residence.
On Wednesday, council members backed a timetable to finish work in time for the September 2019 intake.
It said it has invited the university executive to present a report in October setting out funding options for the project.
Sir Emyr Jones Parry, council chairman and chancellor of the university, said: "Today marks another step forward in our intention to provide fit-for-future accommodation in Pantycelyn for Welsh-medium students coming to Aberystwyth."
Hanna Merrigan, president of the Aberystwyth Welsh Students' Union, welcomed the council's decision.
"The idea of having an appeal to raise funds for the project is a good idea - it's a way of keeping the momentum going," she said.
Plans to reopen halls of residence for Welsh-speaking students at Aberystwyth University have been endorsed.