The side's appearance in France will be its first at a major tournament since the 1958 World Cup.
Players and coaches left their base at the Vale Resort, Vale of Glamorgan, on Saturday and headed to Cardiff Airport.
After a send-off from pupils from Ysgol Treganna, Cardiff, the team took off for a friendly in Sweden on Sunday.
They will then head to France ahead of the team's first game of the tournament against Slovakia on 11 June.
Wales' football team has departed the country as their Euro 2016 preparations reach a climax.