Brown arrived in Ottawa to provide leadership and a solid forward-line presence for the Senators after establishing himself as a hard-working team player in four seasons with the Toronto Maple Leafs.

He had 99 points (43 goals, 56 assists) in 253 games with the Maple Leafs and five points (one goal, four assists) in 20 NHL playoff games before being traded to the Senators on July 1, 2019.

The forward from Etobicoke, Ontario spent four seasons in junior hockey - one with St. Michael's of the Ontario Junior Hockey League, three with Erie of the Ontario Hockey League. He flourished with Erie as a linemate of Connor McDavid, the No. 1 pick in the 2015 NHL Draft. In 2013-14, his final season with Erie, Brown had 45 goals and 128 points, finishing as the OHL's top scorer and being named its most outstanding player.

The Maple Leafs then sent Brown to their AHL affiliate in Toronto, where he was the league's top rookie scorer with 61 points (21 goals) in 2014-15. The next season he fractured an ankle blocking a shot, which kept him out for 35 games.The Maple Leafs then sent Brown to their AHL affiliate in Toronto, where he was the league's top rookie scorer with 61 points (21 goals) in 2014-15. The next season he fractured an ankle blocking a shot, which kept him out for 35 games.

He returned in the second half of the season and was called up to the Maple Leafs. Brown made his NHL debut March 17, 2016 and got his first NHL point four days later against the Calgary Flames.

He scored his first NHL goal March 24, 2016, against goaltender Frederik Andersen of the Anaheim Ducks, and had three assists in his final League appearance of the season, March 29 against the Florida Panthers. Brown finished with six points in seven games.

Brown became a full-time NHL player in 2016-17, playing in all 82 games for the Maple Leafs and scoring 36 points (20 goals, 16 assists). He followed it up with a 28-point season (14 goals, 14 assists) in 82 games in 2017-18. Brown played in all 82 games for the third straight season in 2018-19 with 29 points (eight goals, 21 assists).

Brown signed a one-year contract with the Edmonton Oilers on July 1, 2023, reuniting him with Connor McDavid from their days playing for Erie in the Ontario Hockey League. He sustained a knee injury four games into the 2022-23 season and had season-ending surgery. He signed a one-year, $1 million contract to stay with the Oilers on July 1, 2024, in lieu of becoming an unrestricted free agent, after he had 12 points (four goals, eight assists) in 71 regular-season games and six points (two goals, four assists) in 19 Stanley Cup Playoff games to help Edmonton reach the Stanley Cup Final, a seven-game loss to the Florida Panthers.

Following another trip to the Final, when the Oilers lost to the Panthers in six games, Brown signed a four-year, $12 million contract with the New Jersey Devils on July 1, 2025.