Shengelia was selected with the 54th overall pick in the 2012 NBA draft by Philadelphia 76ers. He was later traded to the Brooklyn Nets on draft night. In July 2012, he joined the Nets for the 2012 NBA Summer League. In 5 games, he averaged 10.2 points and 3.6 rebounds per game. On July 24, 2012, Shengelia signed with the Nets. During his rookie and sophomore seasons, he had multiple assignments with the Springfield Armor of the NBA D-League.
On June 21, 2014, Shengelia signed a three-year deal with Baskonia. On March 1, 2015, the basque derby with Bilbao Basket finished with a brawl where Dejan Todorović of Bilbao and he were disqualified and twelve players were ejected due to court invasion during the fight. With four seconds left and Bilbao winning by a huge margin, despite the referee's call for a travelling, Todorović was going to dunk when Todorović was hit by him. After this, the Serbian player pushed him from behind and the Georgian forward reacted with a punch. After this, all the players who were in the bench came into the court and started the brawl. When Shengelia was leaving the court after the disqualifying foul, he apologized to a child who was in the first row of the arena. The ACB announced this brawl would have severe consequences and sanctions and would talk with the Spanish Basketball Federation for changing the disciplinary regulations. On March 5, the league provisionally suspended Todorović and Shengelia until the final resolution of the case. Both clubs claimed to have the same sanctions than in 2004, when the brawl Real Madrid and Estudiantes occurred. Finally, on March 11, the Disciplinary Judge accorded to suspend him for five games, Todorović for four and a €3,000 fine to Bilbao Basket player Dairis Bertāns and to Baskonia brothers Mamadou and Ilimane Diop. On June 7, 2017, Shengelia signed a three-year contract extension with Baskonia. Over 33 EuroLeague games, he averaged career-highs of 13.7 points, 6.1 rebounds and 2.2 assists per game. In May 2018, he was named the All-EuroLeague First Team for the 2017–18 season. On 24 May 2018, he finished in second place behind Luka Dončić in voting for the Liga ACB MVP of the season. On August 19, 2018, Shengelia signed a four-year contract extension with Baskonia until 2022.
CSKA Moscow (2020–present)
On July 9, 2020, he signed a three-year contract with Russian club CSKA Moscow. This drew heavy criticism in Georgia, including from the President of Georgia calling it "sad and unacceptable".
