Roslovic's performance during two seasons with the United States National Team Development Program attracted the interest of the Winnipeg Jets, who selected him in the first round (No. 25) of the 2015 NHL Draft. After one season with Miami University, he signed a three-year, entry-level contract with the Jets on July 18, 2016.

Roslovic led Manitoba of the American Hockey League in scoring during the 2016-17 season with 48 points (13 goals, 35 assists) in 65 games. He also made his NHL debut with the Jets in his hometown, Columbus, Ohio, against the Blue Jackets on April 6, 2017.

After scoring 35 points (15 goals, 20 assists) in 35 games for Manitoba in 2017-18, Roslovic earned another recall by the Jets. He scored his first NHL goal against the Anaheim Ducks on Jan. 25, 2018, and finished with 14 points (five goals, nine assists) in 31 games. Roslovic also had three assists in 10 Stanley Cup Playoff games for the Jets, who advanced to the Western Conference Final before losing to the Vegas Golden Knights in five games.

Roslovic had his first NHL hat trick when he scored three power-play goals against the Anaheim Ducks on Feb. 2, 2019.

Roslovic was traded with Patrik Laine to the Columbus Blue Jackets on Jan. 23, 2021, for Pierre-Luc Dubois and a third-round pick in the 2022 NHL Draft and scored an NHL career-high 22 goals in 81 games of the 2021-22 season. He was traded to the New York Rangers on March 8, 2024, for a conditional fourth-round pick in the 2026 NHL Draft.

Roslovic signed a one-year, $2.8 million contract with the Carolina Hurricanes on July 4, 2024. He signed a one-year, $1.5 million contract with the Edmonton Oilers on Oct. 8, 2025.