With the Ottawa 67's in 2011–12, Ceci finished second in scoring amongst all OHL defenceman with 60 points.[6] So eager was Ottawa Senators' GM Bryan Murray to select Ceci that he contacted three different teams early in the 2012 draft in an effort to move up and take the defenceman before another team could. "I honestly never thought he would be available at 15," said Murray.[7] On August 23, 2012, Ceci signed a three-year entry-level contract with the Senators.[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. Ceci did not have NHL callup rights and was thus able to finish the season in junior.[9] Once the Attack were eliminated, Ceci was called up to finish the season in the AHL with the Binghamton Senators, playing in the team's final three games of the regular season. Paired on defence with team captain Mark Borowiecki, he scored his first professional point in his second game with Binghamton and scored his first professional goal a day later in the season finale.[10]
Professional
Ottawa Senators
In October 2013, Ceci was assigned to the Binghamton Senators after training camp. After a suspension to Senators defenceman Jared Cowen, Ceci was called up to Ottawa in December and played his first game in the NHL on December 12, 2013, in Ottawa against the Buffalo Sabres, a 2–1 win for Ottawa. Two games later, on December 16, 2013, at 3:59 of overtime against goaltender Brian Elliott of the St. Louis Blues,[11] Ceci scored his first NHL goal, to win the game 3–2.[12] He was the first teenager in NHL history to score his first NHL goal in overtime.[13] At the beginning of the 2016–17 season, Ceci signed a two-year, $5.6 million contract extension.[14][15] In the 2016–17 season he made 2.25 million and in the 2017–18 season he made 3.35 million.[14]
On August 3, 2018, Ceci agreed to a one-year, $4.3 million contract with the Senators after filing for salary arbitration.
Toronto Maple Leafs
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.[16] Ceci soon agreed to sign a one-year, $4.5 million contract extension with the Maple Leafs on July 4, 2019.[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.[18] However, after suffering an ankle injury in February, the Leafs placed Ceci on injured reserve[19] until March 6, 2020.[20]
Pittsburgh Penguins
On October 17, 2020, Ceci signed as a free agent to a one-year, $1.25 million contract with the Pittsburgh Penguins.[21]
Edmonton Oilers
On July 28, 2021, Ceci signed as a free agent to a four-year, $13 million contract with the Edmonton Oilers. The signing was initiated by the loss of Oilers defenceman Adam Larsson to the Seattle Kraken expansion team, which left a defensive role to be filled by the team.[22] In his first year with the Oilers, he managed 5 goals 23 assists during the regular season.[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.[24] The Oilers were eliminated in the Western Conference Final by the top seeded and eventual Stanley Cup champion Colorado Avalanche.[25]
On November 18, 2009, Ceci was selected by Hockey Canada to compete in the 2010 World U-17 Hockey Challenge for Team Ontario.[27] 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.[28] He would again qualify to compete for Team Canada during the 2011 IIHF World U18 Championship.[29]