The draw was made in Monaco on Friday afternoon, hours after Wolves beat Torino 5-3 on aggregate to seal their passage through the qualifying rounds, with Nuno Espirito Santo's team drawn in Group K.
Besiktas finished third in the Turkish Super Lig last season. They play at the recently-rebuilt Vodafone Park stadium with a capacity of 41,000.
The Turkish side are regulars in the knockout stages of European competitions and reached the last 16 of the Champions League in 2018, as well as the Europa League quarter-finals a year earlier.
Portuguese outfit Braga qualified for the group stage after beating Bronby and Spartak Moscow in their two qualifying ties, after finishing fourth in the Portuguese top flight last season.
They play at the beautiful 30,000-capacity Municipal Stadium of Braga, which is carved into the side of a mountain.
Slovakian champions Slovan Bratislava complete the group. They also had to progress via the qualifiers, beating Feronikeli, Dundalk and POAK to reach the group stages, with the latter tie won on away goals last night.
The fixtures for the group stage matches, which will take place from September to December, will be announced later this afternoon.
The top two teams will qualify for the Europa League knockout phase, which takes place next year.
Group stage fixtures:
Sep 19 Wolves v Braga
Oct 3 - Besiktas v Wolves
Oct 24 - Slovan Bratislava v Wolves
Nov 7 - Wolves v Slovan Bratislava
Nov 28 - Braga v Wolves
Dec 12 - Wolves v Besiktas