The Istanbul-based team accumulated a 162-143 win in two games as Bahcesehir Koleji previously won the first leg 72-69 last week in Italy.
It is the Turkish club's first title in the FIBA Europe Cup, and the first trophy in the club's history.
Bahcesehir Koleji were leading the game at Istanbul's Ulker Sports and Event Hall 43-37 by the end of the second quarter.
After Sam Dekker's dunk, Bahcesehir Koleji extended the gap to 10 points, 68-58, in the early minutes of the fourth quarter as the Turkish team had control of the game until the final buzzer.
US shooting guard Jamar Smith led Bahcesehir Koleji, scoring 17 points against Unahotels Reggio Emilia.
He was named the MVP (Most Valuable Player) of the final.
Smith also had four assists.
Jamal Jones scored 14 points, and Dekker tallied 12 points for the Turkish club.
In addition, Bahcesehir Koleji center Tarik Black clocked up 12 points.
Arturs Strautins and Stephen Mark Thompson Jr. were the game's top scorers with 19 points each.
Strautins also had 11 rebounds.
Established in 2015, the Europe Cup is organized by FIBA every year. It is FIBA Europe's second-tier basketball tournament in club level.
