A strong skater capable of playing in all situations, Moore was selected by the Columbus Blue Jackets in the first round (No. 21) of the 2009 NHL Draft after he had 39 points, including 14 goals, for Chicago of the United States Hockey League.

During the 2009-10 season, Moore played for Kitchener in the Ontario Hockey League, where he scored 47 points (10 goals, 37 assists) in 61 games and 16 points (four goals, 12 assists) in 20 playoff games.

The Winnetka, Illinois, native turned pro the following season, playing 73 games for Springfield of the American Hockey League. That season, he also made his NHL debut, playing 12:05 for the Blue Jackets in a 4-3 win against the Edmonton Oilers on Feb. 5, 2011.

Moore became a full-time NHL defenseman in 2011-12, when he had seven points (two goals, five assists) in 67 games, but the following season, Columbus traded him to the New York Rangers on April 3, 2013.

Moore found consistent playing time for the Rangers, and in 2013-14, he played in 21 Stanley Cup Playoff games (two assists) to help New York advance to the Cup Final, where it lost to the Los Angeles Kings in five games.

However, Moore was traded for the second time in the NHL on March 1, 2015, when he was acquired by the Arizona Coyotes. After playing 19 with the Coyotes, he signed as a free agent with the New Jersey Devils on July 1, 2015.

Moore would play three seasons in New Jersey, including in 2016-17 when he scored an NHL career-high 12 goals, before signing with the Boston Bruins as a free agent on July 1, 2018.

Moore would play three seasons in New Jersey, including in 2016-17 when he scored an NHL career-high 12 goals, before signing with the Boston Bruins as a free agent on July 1, 2018.

During his first season in Boston, Moore had 13 points (four goals, nine assists) in 61 regular-season games, and he played in 10 playoff games to help the Bruins advance to the Cup Final, where they lost to the St. Louis Blues in seven games.