The tie will see the Saints boss face the team where he began his managerial career.
The Dutchman welcomed the challenge of taking on a club he knows well, having coached there in 2000-2001 before joining Ajax.
Speaking to Southampton’s official YouTube channel, Koeman said: “I already made a joke before the draw that maybe we would go back to Holland again after our pre-season.
“It is nice because it was my first club starting as a head coach, so it is nice to come back.
“But it is okay, it is a good draw, we play against a good team, at least a team who likes to play football, so we will wait to see what happens.
“In the possibilities that we had to draw, maybe it is the worst of that, but it means Europa League football, and we have to show we are a better team than Vitesse and we have two games to do that.
“Now we can say we will go to Holland (for friendly games) and it is good preparation. We can get a good feel about the Dutch league and the Dutch level.”