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The Giallorosse were drawn in Group B of the competition during Friday's draw in Nyon, meaning they will come up against the German champions twice in the coming weeks.
Alessandro Spugna's side will also face Czech champions Slavia Prague in the group; after beating local rivals Sparta Prague over two legs (6-2 on aggregate) to reach this stage of the competition.
The third opponents for Roma will be Austrian side St Polten.
The fixture list for the six group stage games is set to be confirmed in due course.
"Regardless of what the draw has given us we want to focus on how we are going to grow and improve through playing them," said Spugna.
"The games are going to be tough but great to be involved in, we are all excited to be playing in the group stage of this competition.
"Wolfsburg are the most storied team in Europe so it is obviously going to be very interesting to go up against them, but we don't want to underestimate Slavia Prague and St Polten - both of whom have more experience than we do in this competition.
"Playing in the group stage gives us a chance to test ourselves and the way we want to play - something we've done a good job of doing in Serie A - at an even higher and more demanding level."
For the first time in the competition's history there are two Italian sides competing in the group stage: Juventus were drawn in Group C alongside competition holders Lyon, English side Arsenal and Swiss champions Zurich.
Roma are the only group stage debutants in this season's competition.
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