Moore, 27, was officially announced as Scott Pendlebury's successor on Wednesday.
He is the Magpies' 48th AFL/VFL captain, joining a list that includes his father and club great Peter, who skippered Collingwood in 1981-82.
The pair are the second father-son captains in club history, after Charlie Pannam Snr (1905) and his son Alby Pannam (1945).
"It is truly an incredible honour to be given the opportunity to lead this team," Moore said.
"The Collingwood captaincy is significant in its own right but it also holds another layer of significance for my family and I.
"To follow my father's journey as captain of the Collingwood Football Club at almost the same stage in his football journey is very special.
"There's no shortage of strong and up-and-coming leaders in our group, and I look forward to working closely with the individuals that surround me to ensure we all continue to develop as leaders.
"I am fortunate to be part of a team and wider club that features so many selfless and determined individuals."
Moore will be supported by Taylor Adams, Jeremy Howe and Brayden Maynard in a four-man leadership group.
It will be Adams' eighth season in the group and Howe's sixth, while hard-nut Maynard has been elevated after earning his first All-Australian nod last year.
The appointments were ratified by Collingwood's board on Tuesday night, following a player-led process to identify leaders.
"All four players display a strong alignment to the club values as well as attributes that will nurture, mentor and inspire the team," Magpies football boss Graham Wright said.
"This process has confirmed there is no shortage of upcoming leaders in our group.
"We are fortunate to have a number of players who will play a role in leading this team even if they don't hold a formal leadership title."
Pendlebury stepped down in December, having led the Magpies in a club-record 206 games. The 34-year-old will continue playing in 2023.
Moore finished third in the Magpies' best-and-fairest award last season as they reached a preliminary final in Craig McRae's first year as coach.
Meanwhile, versatile tall Darcy Cameron has suffered a fresh hamstring setback in a blow to Collingwood's ruck stocks.
Cameron has just over six weeks to recover before the start of the season, with the Magpies taking on Geelong in round one on March 17.
Mason Cox shapes as Collingwood's next best ruck option after Brodie Grundy joined Melbourne in the off-season.
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