Management and the IMPACT trade union have accepted Labour Court recommendations - to resolve the dispute.
The Transport Minister is welcoming the breakthrough. The development came about following over eight hours of negotiations yesterday.
Last night, Aer Lingus cabin crew called off two strikes next Monday and Wednesday, pending consideration of Labour Court proposals to end a roster dispute.
The recommendations were issued this morning and have been accepted by both sides.
Michael Landers from IMPACT said more negotiations will be required before the row is fully resolved.
Aer Lingus said it will set up a roster-issue technical group, along with implementing the other aspects of the plan.
Welcoming the development, Transport Minister Leo Varadkar said he hopes both sides will engage in talks on the basis set by the Labour Court.