He began his professional career when he signed with the Greek League club Olympiacos Piraeus in 2010.[4] 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 July 1, 2018, Katsivelis was announced by Promitheas Patras, where he subsequently spent two seasons.[7] He averaged 3.7 points, 2.2 rebounds and 1.1 assists per game in the shortened 2019-2020 campaign.
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.