Chris Coleman's side qualified for their first major tournament in 58 years by finishing second in Group B while Northern Ireland topped Group F to reach their first European Championship.
Prior to Euro 2016, Wales will face their near-neighbours at Cardiff City Stadium on March 24 before taking on Northern Ireland's Group C rivals Ukraine at the Olympic Stadium in Kiev four days later.
Wales boss Coleman said: "We are delighted to be playing the two fixtures and they will be ideal preparation for our group games at Euro 2016.
"Michael O'Neill has done a fantastic job as manager of Northern Ireland and I am delighted for him. This will be a great occasion for both sets of fans ahead of the finals.
"Meanwhile, the Ukraine are quality opposition and will be a real test for myself, the coaching team and the squad of players."