Papagiannis made his senior men's club debut with Peristeri on January 5, 2012, at the age of 14, in a Greek Basket League 2011–12 season game against Panathinaikos.

[9] Papagiannis, considered to be one of the biggest young European talent prospects, received scholarship offers from 17 USA colleges, including UConn, Arizona, Temple,[10] NC State,[11] Oregon, St. John's, and Kentucky.

[21] On November 5, 2016, he made his NBA debut in a 117–91 loss to the Milwaukee Bucks, recording two points and one rebound in six minutes off the bench.

Additionally, in 34 domestic league matches, he averaged 9.3 points, 6 rebounds, 1.3 assists and 1.2 blocks in 22 minutes per contest.

On July 14, 2023, after weeks of stagnant negotiations, Papagiannis informed Panathinaikos that he had rejected their contract renewal proposal and he would be leaving the club after a total of seven seasons together.

On July 15, 2023, Papagiannis signed a two-year deal with Turkish powerhouse Fenerbahçe, under his national team coach Dimitrios Itoudis.

With the Greek Under-16 junior national team, Papagiannis played at the 2012 FIBA Europe Under-16 Championship, which he led in blocks per game.

He also played at the 2013 FIBA Europe Under-16 Championship, where he won the bronze medal and was named to the All-Tournament Team,[33] after leading the tournament in blocks per game.