In the summer of 2016, Papagiannis was selected as the 13th pick in the 1st round of the NBA Draft by the Phoenix Suns, making him the highest-picked player in Greek history. He was subsequently traded to the Sacramento Kings after the draft. Papagiannis spent the 2016-17 season with the Sacramento Kings and their G-League team, the Reno Bighorns. He began the 2017-18 season with the Sacramento Kings but moved to the Portland Trail Blazers in March.
Returning to the EuroLeague in the summer of 2018, wearing the Panathinaikos jersey once again, Papagiannis played for the Greens from 2018 to 2023, experiencing his most successful season in 2021-22. He led the EuroLeague in blocks and rebounds with averages of 10.3 points, 8.2 rebounds, 1.7 blocks, and a 17.4 PIR (Performance Index Rating) and was honored with a place on the league's All-Second Team.
In the previous EuroLeague season, Papagiannis maintained averages of 8.5 points, 5.7 rebounds, 1.2 blocks, and an 11.4 PIR, while also serving as the captain of Panathinaikos. According to reports from Sport24.gr and Alexandros Trigkas, the 25-year-old center's earnings will reach 3.5 million euros for his two seasons in Turkey, including bonuses tied to individual and team achievements.
Panathinaikos had offered the player 1.3 million euros for the first year of the contract and 1.7 million euros for the second year, but Papagiannis ultimately chose to join Fenerbahce Beko Istanbul.
