He previously played for the Ottawa Senators, Toronto Maple Leafs, Pittsburgh Penguins, Edmonton Oilers, and San Jose Sharks.

[8] On January 8, 2013, in an effort to overtake the London Knights in the OHL's Western Conference, the Owen Sound Attack obtained Ceci from the 67's.

[14] On August 3, 2018, Ceci agreed to a one-year, $4.3 million contract with the Senators after filing for salary arbitration.

On July 1, 2019, Ceci was traded by the Senators, along with Ben Harpur, Aaron Luchuk and a 2020 third-round draft pick to the Toronto Maple Leafs in exchange for Connor Brown, Michael Carcone and Nikita Zaitsev.

[17] He scored his first goal as a Toronto Maple Leaf on October 4, 2019, in a 4–1 road win over the Columbus Blue Jackets.

[23] During the team's deep run in the 2022 Stanley Cup playoffs, Ceci notably scored the series-clinching goal in Game 7 of the first round series against the Los Angeles Kings.

[25] On August 18, 2024, Ceci was traded to the San Jose Sharks along with a 2025 third-round pick in return for defenceman Ty Emberson.

[28] After the season concluded, Ceci was one of 15 OHL players invited to attend Canada’s National Men’s Summer Under-18 Team selection camp on June 11, 2010.