Katsivelis started his career playing at the
semi-professional level (
the 3rd-tier level of Greek basketball) with Mantoulidis in the
Greek B League. He began his professional career when he signed with the
Greek League club
Olympiacos Piraeus in 2010. With Olympiacos, he won the
EuroLeague and Greek League championships, in 2012. With Olympiacos, he also won the
2012–13 season championship of the EuroLeague, and the Greek League championship in 2015. On August 5, 2015, he signed with
AEK Athens. He moved to the Kazakh club
Astana, of the
VTB United League, for the 2016–17 season. On July 1, 2018, Katsivelis was announced by
Promitheas Patras, where he subsequently spent two seasons. He averaged 3.7 points, 2.2 rebounds and 1.1 assists per game in the shortened 2019-2020 campaign. On August 8, 2020, he agreed to return to
AEK. On July 24, 2021, Katsivelis moved to
Peristeri. On April 18, 2022, he was suspended for the rest of the season, along with teammate
Linos Chrysikopoulos, after they both fell out of favor with the club's new head coach
Milan Tomić. In 17 league games, he averaged 6.7 points, 2.1 rebounds and 3 assists per contest. On August 25, 2022, Katsivelis signed with
Kolossos Rodou, reuniting with both Chrysikopoulos and his Astana coach
Ilias Papatheodorou. In 24 games, he averaged 7.6 points, 3.7 rebounds, 3.8 assists and 1.5 steals, playing around 26 minutes per contest. On June 30, 2023, Katsivelis returned to Thessaloniki for
Aris. On June 28, 2024, Katsivelis returned to PAOK, and was named the team's captain. On July 4, 2025, Katsivelis returned Athens for a third stint with
AEK Athens, signing a two year contract. ==National team career==