Bratt was selected by the Devils in the sixth round (No. 162) of the 2016 NHL Draft after he scored four points (two goals, two assists) in seven games for Sweden at that year's Under-18 5-Nations Tournament.

After signing a three-year, entry-level contract with the Devils on May 13, 2017, he became the lowest drafted teenager to play in the NHL since 1995-96, when center Roman Vopat (No. 172, 1994) and forward Richard Zednik (No. 249, 1994) played for the St. Louis Blues and Washington Capitals, respectively.

Bratt scored his first NHL goal in his debut against the Colorado Avalanche on Oct. 7, 2017. He scored two more goals in his second game at the Buffalo Sabres two days later. He finished the 2017-18 season with 35 points (13 goals, 22 assists) in 74 games.

He had an NHL career high 16 goals in 2019-20 before the season paused March 12 due to concerns surrounding the coronavirus.

Bratt agreed to a one-year, $5.45 million contract with the Devils on Aug. 3, 2022. He was a restricted free agent and avoided a salary arbitration hearing after leading New Jersey in assists (47) and points (73) in 76 games and tying Jack Hughes for the team lead in goals (26). Bratt's assist in a 5-2 win against the Vancouver Canucks on Nov. 1, 2022, gave him 16 points (four goals, 12 assists) in a 10-game point streak that tied Tim Higgins' Devils/Colorado Rockies/Kansas City Scouts record (Oct. 12-Nov. 2, 1984) to start a season. His run ended with a new franchise record of 11 in a 4-3 overtime win at the Calgary Flames on Nov. 5.

Bratt ended the season with 73 points (32 goals, 41 assists) and six points (one goal, five assists) in 12 Stanley Cup Playoff games. He signed an eight-year, $63 million contract with the Devils on June 15, preventing him from becoming a restricted free agent.

Bratt was named to Sweden's roster for the 4 Nations Face-Off during the 2024-25 season.