United play the first leg at Balaidos on May 4 with the return leg at Old Trafford on May 11. In the other semi-final Ajax take on Lyon with the first leg in Amsterdam.
United have never played the Spanish outfit before in any competition but will consider themselves in the driving seat against a Celta side mid-table in La Liga.
United boss Jose Mourinho is looking to win the Europa League in order to secure passage into next season's Champions League.
The final in Stockholm at the Friends Arena takes place on May 24.