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. He became the youngest player to ever play in the modern era of the Greek Basket League. He also spent the entire 2012–13 season with Peristeri.
Panathinaikos (2014–2016)
On June 25, 2014, Papagiannis signed with Panathinaikos on a multi-year deal, yet there was a player option in the contract, which allowed him to leave Panathinaikos for a US college during the summer of 2015. Papagiannis, considered to be one of the biggest young European talent prospects, received scholarship offers from 17 USA colleges, including UConn, Arizona, Temple, NC State, Oregon, St. John's, and Kentucky. On July 8, 2015, it was announced that Papagiannis had chosen to continue playing for Panathinaikos. His Panathinaikos contract included a €500,000 euros buyout option. Papagiannis was a member of the Panathinaikos teams that won both the 2015 edition and the 2016 edition of the Greek Cup. He also played in six games with Panathinaikos during the 2015–16 EuroLeague season competition, where he averaged 1.5 points and 1.7 rebounds per game, in 5 minutes per game. In the 2015–16 Greek League season, he averaged 6.5 points and 2.8 rebounds per game, in 11.5 minutes per game, in 23 games played.
Sacramento Kings (2016–2018)
In April 2016, Papagiannis entered the 2016 NBA draft, and was projected as a mid-to-late second round pick, but he also garnered interest as a late first round pick. However, on June 23, Papagiannis was selected with the 13th overall pick by the Phoenix Suns, becoming the highest drafted Greek player ever. His rights were later traded to the Sacramento Kings on draft night, and in July, he joined the Kings for the 2016 NBA Summer League. On July 15, 2016, he signed his rookie scale contract with the Kings. 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. On March 18, 2017, he had his first double-double with 14 points and 11 rebounds in the Kings' 110–94 loss to the Oklahoma City Thunder. During his rookie season, he had multiple assignments with the Reno Bighorns of the NBA Development League. On February 8, 2018, Papagiannis was waived by the Sacramento Kings.
On March 8, 2018, Papagiannis signed a 10-day contract with the Portland Trail Blazers. Despite not playing a single game for Portland at the end of his 10-day contract, Papagiannis signed a two-year contract on March 18. He appeared in one game with the Blazers. Papagiannis was waived by the Blazers after the end of the 2018 NBA Summer League.
Return to Panathinaikos (2018-present)
On July 20, 2018, Papagiannis officially returned to Panathinaikos, after signing a contract with the team for 5 years, with the last 2 years of the contract being team options. The contract also included an NBA opt-out option, after the third year of the contract.
